Question

Cho các biểu thức

a) rút gọn A và B

b) tìm x để A . B = -1

B = \(\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}+\frac{2\sqrt{x}-1}{4-x}\)

A = \(10-\left(\sqrt{32}-\sqrt{8}-\sqrt{27}\right)\left(\sqrt{8}-\sqrt{32}-\sqrt{27}\right)\)

Answer 1

ĐKXĐ: \(x\ge0;x\ne4\)

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

\(=\frac{\sqrt{x}+2+\sqrt{x}-2-2\sqrt{x}+1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{1}{x-4}\)

\(A=10-\left(2\sqrt{2}-3\sqrt{3}\right)\left(-2\sqrt{2}-3\sqrt{3}\right)\)

\(=10+\left(2\sqrt{2}-3\sqrt{3}\right)\left(2\sqrt{2}+3\sqrt{3}\right)\)

\(=10+\left(8-27\right)=-9\)

\(AB=-1\Leftrightarrow\frac{-9}{x-4}=-1\Rightarrow x-4=9\Rightarrow x=13\)