Chapter 8.2, Problem 53HP

To determine

To find: The correct value of x by solving the equation $\left(ax+b\right)\left(ax-b\right)=0$ .

Answer to Problem 53HP

The required value of x is $\frac{b}{a}$ .

Explanation of Solution

Given information:

The given equation is

  $\left(ax+b\right)\left(ax-b\right)=0$

Consider the given equation of height as $\left(ax+b\right)\left(ax-b\right)=0$

Solve the above equation to find the value of x .

  $\begin{array}{c}\left(ax+b\right)\left(ax-b\right)=0\\ {\left(ax\right)}^2-b^2=0\\ a^2{x}^2=b^2\\ x^2=\frac{b^2}{a^2}\end{array}$

Find the root of the above equation.

  $\begin{array}{c}{x}^2=\frac{b^2}{a^2}\\ x=\sqrt{\frac{b^2}{a^2}}\\ =\frac{b}{a}\end{array}$

From the above solution, it is seen that the value of b is x times a and the value of a is b by x .

Hence, the required value of x is $\frac{b}{a}$ .