waecmaths question:
If ${{2}^{a}}=\sqrt{64}$ and $\frac{b}{a}=3$, evaluate ${{a}^{2}}+{{b}^{2}}$
Option A:
250
Option B:
160
Option C:
90
Option D:
48
waecmaths solution:
$\begin{align} & {{2}^{a}}=\sqrt{64} \\ & {{2}^{a}}=8={{2}^{3}} \\ & a=3 \\ & \frac{b}{a}=3 \\ & b=3a \\ & \text{Substitute }3\text{ for }a\text{ in }b=3a \\ & b=3(3)=9 \\ & {{a}^{2}}+{{b}^{2}}={{3}^{2}}+{{9}^{2}}=90 \\\end{align}$
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