Answer Key 9.11

Terrance Berg

Answer Key 9.11

First, the roots:

\begin{array}{ccc} 3 \\ 44 \\ 8 & 4 \end{array}

$\begin{array}{ccc}&3& \\ &\textbf{44}& \\ 8&&4\end{array}$

\begin{array}{ccc} 9 \\ 32 \\ 7 & 2 \end{array}

$\begin{array}{ccc}&9& \\ &\textbf{32}& \\ 7&&2\end{array}$

\begin{array}{ccc} 8 \\ 75 \\ 7 & \sqrt{x} \end{array}

$\begin{array}{ccc}&8& \\ &\textbf{75}& \\ 7&&\sqrt{x} \end{array}$

Check for pattern in the first box:

$3\cdot 8+4=28$
$4\cdot 8\cdot 3=35$
$(8+3)\cdot 4=44\checkmark$

Check #3 pattern with the next box:

$(7+9)\cdot 2=32\checkmark$

Finally:

$\begin{array}{rrl} (7+8)\sqrt{x}&=&75 \\ \\ 15\sqrt{x}&=&75 \\ \\ \dfrac{15}{15}\sqrt{x}&=&\dfrac{75}{15} \\ \\ \sqrt{x}&=&5 \\ \\ \therefore (\sqrt{x})^2&=&(5)^2 \\ \\ x&=&25 \end{array}$

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