While solving an equation I get 2 answers, but when I substitute one of the answers the equality doesn't hold?

Question

I solved the following equation: $$\sqrt{x + 1} + \sqrt{2 \cdot x + 3} - \sqrt{8 \cdot x + 1} = 0$$ I get 2 answers $3,-1/17$ but when I plug $-1/17$ on the equation the equality is wrong.

Answer 1

For your equation must you demand $$x\geq -1$$ and $$x\geq -\frac{3}{2}$$ and $$x\geq -\frac{1}{8}$$ because of the existence of the square roots in your equation. After squaring one times we obtain $$2\sqrt{x+1}\sqrt{2x+3}=5x-3$$ you can only square again if $$x\geq \frac{3}{5}$$