Answer Key 9.11

First, the roots:

    \[\begin{tabular}{|c|c|c|} \hline \begin{array}{ccc}&3& \\ &\textbf{44}& \\ 8&&4\end{array}& \begin{array}{ccc}&9& \\ &\textbf{32}& \\ 7&&2\end{array}& \begin{array}{ccc}&8& \\ &\textbf{75}& \\ 7&&\sqrt{x} \end{array}\\ \hline \end{tabular}\]

Check for pattern in the first box:

  1. 3\cdot 8+4=28
  2. 4\cdot 8\cdot 3=35
  3. (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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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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