Question

Helppppppp

\(\sqrt{x+8} - \sqrt{5x + 2} + 2 = 0\)

Answer 1

\(\sqrt{x+8}-\sqrt{5x+2}+2=0\)             

<=> \(\sqrt{x+8}=\sqrt{5x+2}-2\)

<=> x + 8 = \(\left(\sqrt{5x+2}-2\right)^2\)

<=> x + 8 = \(\left(\sqrt{5x+2}\right)^2-4\sqrt{5x+2}+4\)

<=> x + 8 = 5x + 2 - \(4\sqrt{5x+2}+4\)

<=> \(4\sqrt{5x+2}=5x+2+4-x-8\)

<=> \(4\sqrt{5x+2}=4x-2\)

<=> \(4\sqrt{5x+2}=2\left(2x-1\right)\)

<=> \(\sqrt{5x+2}=\dfrac{2\left(2x-1\right)}{4}\)

<=> \(\sqrt{5x+2}=\dfrac{2x-1}{2}\)

<=> 5x + 2 = \(\dfrac{\left(2x-1\right)^2}{4}\)

<=> x = \(\dfrac{\dfrac{\left(2x-1\right)^2}{4}-2}{5}\)

<=> x = -0,278.....