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

User Pusle
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1 Answer

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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.}

User Aagjalpankaj
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