Chapter 1.2, Problem 68PFA

To determine

To evaluate: the given expression.

Answer to Problem 68PFA

  $\frac{6a-b^2}{2}+{\left(\frac{b}{a}\right)}^2=2$

Explanation of Solution

Given information:

Consider the expression $\frac{6a-b^2}{2}+{\left(\frac{b}{a}\right)}^2;a=2,b=4$

Calculations:

Consider $\frac{6a-b^2}{2}+{\left(\frac{b}{a}\right)}^2$

substitute $a=2,b=4$

  $\begin{array}{l}\frac{6a-b^2}{2}+{\left(\frac{b}{a}\right)}^2\\ =\frac{6(2)-{(4)}^2}{2}+{\left(\frac{4}{2}\right)}^2\\ =\frac{12-16}{2}+{\left(2\right)}^2\\ =\frac{-4}{2}+4\\ =-2+4\\ =2\end{array}$

Hence, $\frac{6a-b^2}{2}+{\left(\frac{b}{a}\right)}^2=2$