Solve each equation:the square root of x(x+1)=0

Question

asked Dec 9, 2023 35.8k views

1 Answer

Aagjalpankaj · Answer 1 · 2023-12-14T00:38:56+0000

Recall that:

$\sqrt[]{c}=0\text{ if and only if c=0.}$

Therefore:

$\sqrt[]{x(x+1)}=0\text{ if and only if x(x+1)=0.}$

Now, recall that:

$ab=0\text{ if and only if a=0 or b=0.}$

Therefore:

$x=0\text{ or x+1=0.}$

Solving the last equation for x we get:

$\begin{gathered} x+1-1=0-1, \\ x=-1. \end{gathered}$

Answer: The solutions of the given equation are:

$x=0\text{ and x=-1.}$