Chapter 7.4, Problem 48E

To determine

To find: $a^2+b^2$ by using the given information.

Answer to Problem 48E

70

Explanation of Solution

Given information:

  $\begin{array}{l}{\left(a-b\right)}^2=64\end{array}$

  $\begin{array}{c}ab=3\end{array}$

Calculation:

The value of $a^2+b^2$ can be evaluated as follows:

  $\begin{array}{c}{\left(a-b\right)}^2=a^2+b^2-2ab\end{array}$

  $\begin{array}{c}64=\left(a^2+b^2\right)-2\left(3\right)\left[\text{Put the value of }{\left(a-b\right)}^2\text{ and }ab\right]\end{array}$

  $\begin{array}{c}64=a^2+b^2-6\end{array}$

  $\begin{array}{c}64+6=a^2+b^2\end{array}$

  $\begin{array}{c}70=a^2+b^2\end{array}$

Thus the value of $a^2+b^2$is 70.