Question

giải phương trình sau

\(2.\left(\dfrac{4}{3-\sqrt{x}}\right)^2=2\)

Answer 1

đk x > = 0 ; x khác 9 \(\left(\dfrac{4}{3-\sqrt{x}}\right)^2=1\)

TH1 : \(\dfrac{4}{3-\sqrt{x}}=1\Rightarrow3-\sqrt{x}=4\Leftrightarrow\sqrt{x}=-1\)*vô lí*

TH2 : \(\dfrac{4}{3-\sqrt{x}}=-1\Rightarrow4=\sqrt{x}-3\Leftrightarrow\sqrt{x}=7\Leftrightarrow x=49\left(tm\right)\)

Answer 2

\(2\left(\dfrac{4}{3-\sqrt{x}}\right)^2=2\) \(\left(đk:x\ne9;x\ge0\right)\)

\(\left(\dfrac{4}{3-\sqrt{x}}\right)^2=1\)

\(\left[{}\begin{matrix}\dfrac{4}{3-\sqrt{x}}=1\\\dfrac{4}{3-\sqrt{x}}=-1\end{matrix}\right.\)

\(\left[{}\begin{matrix}3-\sqrt{x}=4\\\sqrt{x}-3=4\end{matrix}\right.\)

\(\left[{}\begin{matrix}\sqrt{x}=-1\left(L\right)\\\sqrt{x}=7\end{matrix}\right.\)

\(x=49\)