Question

[asmr]

cho 2 bieu thuc:

A=(\(\sqrt{20}\) -\(\sqrt{45}\) +3\(\sqrt{5}\) ).\(\sqrt{5}\)  va B=\(\dfrac{x+1-2\sqrt{x}}{\sqrt{x}-1}\) +\(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\) (Dieu kien: x>0, x  khac 1

a) Rut gon bieu thuc A va B

b)Tim cac gia tri cua x de gia tri cua bieu thuc A bang 2lan gia tri B

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(A=\left(2\sqrt{5}-3\sqrt{5}+3\sqrt{5}\right)\cdot\sqrt{5}=2\sqrt{5}\cdot\sqrt{5}=10\)

\(B=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}-1}+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\)

\(=\sqrt{x}-1+\sqrt{x}=2\sqrt{x}-1\)

b: A=2B

=>\(10=4\sqrt{x}-2\)

=>\(4\sqrt{x}=12\)

=>x=9(nhận)