Question

√x-2 - √9-18 + 4=0

Answer 1

Ta có: \(\sqrt{x-2}-\sqrt{9x-18}+4=0\)

\(\Leftrightarrow x-2=4\)

hay x=6

Answer 2

\(\sqrt{x-2}-\sqrt{9x-18}+4=0\)             ĐKXĐ: \(x\ge2\)

<=> \(\sqrt{x-2}=\sqrt{9x-18}-4\)

<=> \(x-2=\left(\sqrt{9x-18}-4\right)^2\)

<=> \(x-2=\left(9x-18\right)-8\sqrt{9x-18}+16\)

<=> \(x-2-9x+18-16=-8\sqrt{9x-18}\)

<=> \(-8x=-8\sqrt{9x-18}\)

<=> \(\sqrt{9x-18}=\dfrac{-8x}{-8}\)

<=> \(\sqrt{9x-18}=x\)

<=> 9x - 18 = x²

<=> x² - 9x + 18 = 0

<=> x² - 3x - 6x + 18 = 0

<=> x(x - 3) - 6(x - 3) = 0

<=> (x - 6)(x - 3) = 0

<=> \(\left[{}\begin{matrix}x-6=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\left(tm\right)\\x=3\left(tm\right)\end{matrix}\right.\)

Vậy nghiệm của PT là S = \(\left\{3;6\right\}\)