Question

1.17 ạ

Answer 1

1.17:

a: \(P=\dfrac{x-7}{\sqrt{x}\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\)

\(=\dfrac{x-7-x+9}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{2}{\sqrt{x}\left(\sqrt{x}-3\right)}\)

b: \(Q=P:\dfrac{1}{\sqrt{x}-3}=\dfrac{2}{\sqrt{x}\left(\sqrt{x}-3\right)}\cdot\dfrac{\sqrt{x}-3}{1}=\dfrac{2}{\sqrt{x}}\)

\(x=\dfrac{2}{10-3\sqrt{11}}=\dfrac{2\left(10+3\sqrt{11}\right)}{100-99}=20+6\sqrt{11}=\left(\sqrt{11}+3\right)^2\)

Khi x=(căn 11+3)^2 thì \(Q=\dfrac{2}{\sqrt{11}+3}=\sqrt{11}-3\)