( 2 n + 1 ) ^{2} - 4 a ^{2} =

8d:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["\t․․․․․․․․․ ㉡\n㉡을 ㉠에 대입하여 변형하면\n\t",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f6"}}],"\n\t",["$","span","p0-1-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f7"}}],"\n(나)"]}] f8:T89d,

( 2 n + 1 + 2 a ) ( 2 n + 1 - 2 a ) =

8e:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["\t",["$","span","p0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f8"}}],"\n(나)"]}] f9:T7c6,

2 n + 1 + 2 a , 2 n + 1 - 2 a

8f:["$","p","p0-3",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["따라서 ",["$","span","p0-3-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$f9"}}],"는\n(다)"]}] fa:T84c,

\displaystyle \sqrt{n ( n + 1 )}

90:["$","p","p0-4",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["이 때, 어느 경우에나 모순이므로 ",["$","span","p0-4-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$fa"}}],"은 유리수가 아니다."]}] 91:["$","p","p0-5",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["위의 증명에서 (가), (나), (다)에 알맞은 것은? [3점]\n (가) (나) (다)\n① ",["$","span","p0-5-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}]," ",["$","span","p0-5-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

4

"}}]," 모두 ",["$","span","p0-5-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}],"이거나 모두 ",["$","span","p0-5-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

- 2

"}}],"이다.\n② ",["$","span","p0-5-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

2

"}}]," ",["$","span","p0-5-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

4

"}}]," 모두 ",["$","span","p0-5-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}],"이거나 모두 ","$Lfb","이다.\n③ ","$Lfc"," ","$Lfd"," 모두 ","$Lfe","이거나 모두 ","$Lff","이다.\n④ ","$L100"," ","$L101"," 모두 ","$L102","이거나 모두 ","$L103","이다.\n⑤ ","$L104"," ","$L105"," 모두 ","$L106","이거나 모두 ","$L107","이다."]}] 92:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{P}

"}}] 108:T49d,

\mathrm{\angle} AOB = 3 \angle APB

93:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$108"}}] 94:["$","img","p0-0-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image5-H8I1vZ9wxjXrWsUSsJcMOZBY1qO4zB.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"13cqw"}}] 109:T6b5,

\displaystyle \mathrm{\overline{AD}} / / \overline{GF}

95:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["[증명]\n 두 직선",["$","span","p0-1-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{AP}

"}}],",",["$","span","p0-1-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{EF}

"}}],"의 교점을",["$","span","p0-1-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{G}

"}}],"라 하면\n",["$","span","p0-1-t0-m7",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$109"}}],",","$L10a","이므로","$L10b","\n또","$L10c","\n(가)"]}] 10d:T45a,

\displaystyle \mathrm{\overline{G E}} =

96:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["이므로",["$","span","p0-2-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$10d"}}],"\n(가)"]}] 10e:T452,

\mathrm{\angle} EGA = \angle EAG

10f:T679,

\mathrm{\angle} EGA + \angle EAG = \angle AEF

97:["$","p","p0-3",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["따라서",["$","span","p0-3-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{\\triangle} EGA

"}}],"는 이등변삼각형이므로",["$","span","p0-3-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10e"}}],"이다.\n\t",["$","span","p0-3-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$10f"}}],",","$L110","이므로\n\t","$L111","\n(나)"]}] 112:T6f9,

\displaystyle \mathrm{\overline{PA}} / / \overline{OE}

113:T6f9,

\displaystyle \mathrm{\overline{PB}} / / \overline{OF}

98:["$","p","p0-4",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["\t∴",["$","span","p0-4-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$112"}}],"\n같은 방법으로",["$","span","p0-4-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$113"}}],"\n\t∴","$L114","\n(다)"]}] 115:T6e9,

\displaystyle = \frac{1}{3} \mathrm{\angle} AOB

116:T49d,

\mathrm{\angle} AOB = 3 \angle APB

99:["$","p","p0-5",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-5-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$115"}}],"\n그러므로",["$","span","p0-5-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$116"}}],""]}] 9a:["$","p","p0-6",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["위의 증명에서 (가), (나), (다)에 알맞은 것은? [4점]\n (가) (나) (다)\n① ",["$","span","p0-6-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"

\\displaystyle \\mathrm{\\overline{GA}}

"}}]," ",["$","span","p0-6-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{\\angle} OEF

"}}]," ",["$","span","p0-6-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{\\angle} EOF

"}}],"\n② ",["$","span","p0-6-t0-m7",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"

\\displaystyle \\mathrm{\\overline{AE}}

"}}]," ","$L117"," ","$L118","\n③ ","$L119"," ","$L11a"," ","$L11b","\n④ ","$L11c"," ","$L11d"," ","$L11e","\n⑤ ","$L11f"," ","$L120"," ","$L121",""]}] 9d:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\omega

"}}] 9e:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}] 9f:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

- \\omega

"}}] a0:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

- \\omega ^{2}

"}}] a1:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

- 1

"}}] 122:T44e,

2 x + y = 10

a3:["$","span","p0-1-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$122"}}] 123:T44f,

x + 3 y = 10

a4:["$","span","p0-1-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$123"}}] 124:T476,

2 x + 3 y = 14

a5:["$","span","p0-1-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$124"}}] 125:T476,

3 x + 2 y = 16

a6:["$","span","p0-1-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$125"}}] 126:T864,

f ^{3} ( x ) = f ( f ^{2} ( x ) )

a9:["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$126"}}] 127:T867,

f ^{10} ( x ) = f ( f ^{9} ( x ) )

aa:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$127"}}] 128:T408,

f ^{10} ( 1 )

ab:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$128"}}] 129:T509,

\displaystyle \frac{1}{10}

ac:["$","span","p0-0-t0-m11",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$129"}}] 12a:T509,

\displaystyle \frac{9}{10}

ad:["$","span","p0-0-t0-m13",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$12a"}}] 12b:T509,

\displaystyle \frac{10}{9}

ae:["$","span","p0-0-t0-m15",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$12b"}}] 12c:T509,

\displaystyle \frac{1}{11}

af:["$","span","p0-0-t0-m17",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$12c"}}] 12d:T50c,

\displaystyle \frac{10}{11}

b0:["$","span","p0-0-t0-m19",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$12d"}}] b2:["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}} ( a , b )

"}}] b3:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image8-xzX1KftSUSvfN8PqvpQ7t5JF7huElJ.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"18cqw"}}]]}] b4:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-2-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image9-rUsIiGnpAZFUcReayWnvZnIBVjFxP0.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"17cqw"}}]]}] b5:["$","p","p0-3",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["③\t④"]}] b6:["$","p","p0-4",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-4-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image10-j8YpPGGlMBRGGpIPYiDo0nSKKkMB4C.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"16cqw"}}]]}] b7:["$","p","p0-5",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-5-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image11-OvAUWUyUsg3nHYZ4Ltycr9IBMVgSwl.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"16cqw"}}]]}] b8:["$","p","p0-6",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["⑤"]}] b9:["$","p","p0-7",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-7-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image12-V1djvPk55YL8wehnNIXAwTwHlDle4J.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"17cqw"}}]]}] ba:["$","p","p0-5",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["③\t④"]}] bb:["$","p","p0-6",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-6-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image19-sKvbve5Itq4AVgNaiyVRGXFnx0qiU7.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"18cqw"}}]]}] bc:["$","p","p0-7",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-7-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image20-xH1YlGugsG47yO5o5QtSbLjTR8A2RD.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"18cqw"}}]]}] bd:["$","p","p0-8",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["⑤"]}] be:["$","p","p0-9",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-9-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/567/image21-NQ5wqfdiMEomAh8S2viCEhBq37B3Fg.jpg","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"18cqw"}}]]}] c1:["$","span","p0-0-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

3 x + 2 y

"}}] 12e:T81a,

\displaystyle i = \sqrt{- 1}

c2:["$","span","p0-0-t0-m7",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$12e"}}] c6:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a , b , c

"}}] 12f:T411,

a + b + c

c7:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$12f"}}] c8:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{O}

"}}] ca:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}} ( a , b )

"}}] cb:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\mathrm{A}

2003년-12월-고1-수학영역