Answer Key 9.11
First, the roots:
| [latex]\begin{array}{ccc}&3& \\ &\textbf{44}& \\ 8&&4\end{array}[/latex] | [latex]\begin{array}{ccc}&9& \\ &\textbf{32}& \\ 7&&2\end{array}[/latex] | [latex]\begin{array}{ccc}&8& \\ &\textbf{75}& \\ 7&&\sqrt{x} \end{array}[/latex] |
Check for pattern in the first box:
- [latex]3\cdot 8+4=28[/latex]
- [latex]4\cdot 8\cdot 3=35[/latex]
- [latex](8+3)\cdot 4=44\checkmark[/latex]
Check #3 pattern with the next box:
[latex](7+9)\cdot 2=32\checkmark[/latex]
Finally:
[latex]\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}[/latex]
