MathRevolution wrote:

[GMAT math practice question]

If x-5=√x+√5 , which of followings is true?

A. x^2+12x+16 = 0

B. x^2-12x+16 = 0

C. x^2+6x+8 = 0

D. x^2-6x+8 = 0

E. x^2+6x-8 = 0

\((\sqrt{x})^2-(\sqrt{5})^2=\sqrt{x}+\sqrt{5}\)

\((\sqrt{x}+\sqrt{5})(\sqrt{x}-\sqrt{5})=(\sqrt{x}+\sqrt{5})\)

\(\sqrt{x}-\sqrt{5}=1\) (\(\sqrt{x}+\sqrt{5}>0\), so it can be divided from both sides)

\(\sqrt{x}=1+\sqrt{5}\), square both sides to get

\(x=6+2\sqrt{5} =>x-6=2\sqrt{5}\), again square both sides and solve it to get

\(x^2-12x+16=0\)

Option

B