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Solve the equation. Write all proposed solutions. Cross out those that are extraneous.

9aa=3\sqrt { 9 - a } - a = 3


Answered 1 year ago
Answered 1 year ago
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Evaluating the given radical equation, we,

9a=3+aAdd a both sides(9a)2=(a+3)2Square both sides9a=a2+6a+9Expand the perfect square0=a2+7aAdd a and 9 both sides0=a(a+7)Factora=0    or    a+7=0Set each factor equal to 0a=0    or    a=7\begin{aligned} \sqrt{9-a}&=3+a&&\texttt{Add $a$ both sides}\\(\sqrt{9-a})^{2}&=(a+3)^{2}&&\texttt{Square both sides}\\9-a&=a^{2}+6a+9&&\texttt{Expand the perfect square}\\0&=a^{2}+7a&&\texttt{Add $a$ and $-9$ both sides}\\0&=a(a+7)&&\texttt{Factor}\\a=0~~~~ &\texttt{or}~~~~a+7=0&&\texttt{Set each factor equal to 0}\\a=0~~~~&\texttt{or}~~~~a=-7 \end{aligned}

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