Câu 1: Giải phương trình:
a) \(\sqrt{x}+\sqrt{2-x}=2\)
b) \(\sqrt{4x-12}+\frac{1}{3}\sqrt{9x-27}=4+\sqrt{x-3}\)
c) \(6\sqrt{4x+8}-\sqrt{9x+18}-2\sqrt{x+2}=21\)
d) \(\left(3-2\sqrt{x}\right)\left(2+3\sqrt{x}\right)=16-6x\)
Câu 2: Cho \(\sqrt{3-x}+\sqrt{5-x}=2\)
Hãy tính: \(A=\sqrt{3-x}-\sqrt{5-x}\)
Bài 2 :
ĐKXĐ : \(\left\{{}\begin{matrix}x\le3\\x\le5\end{matrix}\right.\)
=> \(x\le3\)
Ta có : \(\sqrt{3-x}+\sqrt{5-x}=2\)
=> \(\sqrt{3-x}=2-\sqrt{5-x}\)
=> \(3-x=4-4\sqrt{5-x}+5-x\)
=> \(-4\sqrt{5-x}=-6\)
=> \(\sqrt{5-x}=\frac{3}{2}\)
=> \(x=2,75\) ( TM )
Ta có : \(A=\sqrt{3-2,75}-\sqrt{5-2,75}=-1\)
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