Question

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

Answer 1

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.}`