Giúp e giải câu 61 62 đi ạ
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23.\(\sqrt{14-2\sqrt{33}}=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\left|\sqrt{11}-\sqrt{3}\right|=\sqrt{11}-\sqrt{3}\)
28. \(\sqrt{25-4\sqrt{6}}=\sqrt{\left(2\sqrt{6}\right)^2-2.2\sqrt{6}.1+1^2}=\sqrt{\left(2\sqrt{6}-1\right)^2}\)
\(=\left|2\sqrt{6}-1\right|=2\sqrt{6}-1\)
29.\(\sqrt{14-8\sqrt{3}}=\sqrt{14-2\sqrt{48}}=\sqrt{\left(\sqrt{8}\right)^2-2\sqrt{6}.\sqrt{8}+\left(\sqrt{6}\right)^2}\)
\(=\sqrt{\left(\sqrt{8}-\sqrt{6}\right)^2}=\left|\sqrt{8}-\sqrt{6}\right|=\sqrt{8}-\sqrt{6}\)
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Ta có: AA'\(\perp\)(ABCD) (giả thiết).
Suy ra, (ABCD)\(\perp\)(ACC'A').
Vậy góc tạo bởi hai mặt phẳng đã cho là 90o.
Chọn D.
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11.
Do \(\lim\limits_{x\rightarrow2^-}\left(1-x^2\right)=1-2^2=-3< 0\)
\(\lim\limits_{x\rightarrow2^-}\left(x-2\right)=0\)
Và: \(x-2< 0\) khi \(x< 2\)
\(\Rightarrow\lim\limits_{x\rightarrow2^-}\dfrac{1-x^2}{x-2}=+\infty\)
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Bài 1:
3: ĐKXĐ: x>=1
\(x-\sqrt{x+3+4\sqrt{x-1}}=1\)
=>\(x-\sqrt{x-1+2\cdot\sqrt{x-1}\cdot2+4}=1\)
=>\(x-\sqrt{\left(\sqrt{x-1}+2\right)^2}=1\)
=>\(x-\left|\sqrt{x-1}+2\right|=1\)
=>\(x-\left(\sqrt{x-1}+2\right)=1\)
=>\(x-\sqrt{x-1}-2-1=0\)
=>\(x-1-\sqrt{x-1}-2=0\)
=>\(\left(\sqrt{x-1}\right)^2-2\sqrt{x-1}+\sqrt{x-1}-2=0\)
=>\(\left(\sqrt{x-1}-2\right)\left(\sqrt{x-1}+1\right)=0\)
=>\(\sqrt{x-1}-2=0\)
=>\(\sqrt{x-1}=2\)
=>x-1=4
=>x=5(nhận)
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6.
SAB cân tại S \(\Rightarrow SH\perp AB\)
Mà \(\left\{{}\begin{matrix}AB=\left(SAB\right)\cap\left(ABCD\right)\\\left(SAB\right)\perp\left(ABCD\right)\end{matrix}\right.\) \(\Rightarrow SH\perp\left(ABCD\right)\)
Hay SH alf đường cao của chóp
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61B
62B