Chapter 9.4, Problem 24PPS

To determine

Find the solution.

Answer to Problem 24PPS

$p=4$ or $p=26$

Explanation of Solution

Given Information: ${\left(p-15\right)}^2=121$

Formula Used: $a^2-b^2=(a+b)(a-b)$

Calculation:

  ${\left(p-15\right)}^2=121$

So,

  ${\left(p-15\right)}^2-121=0$

Now, square root of 121 is 11.

  ${\left(p-15\right)}^2-{\left(11\right)}^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $\left(p-15+11\right)\left(p-15-11\right)=0$

Now,

  $\left(p-4\right)\left(p-26\right)=0$

Now,

$p-4=0$ or $p-26=0$

Hence,

$p=4$ or $p=26$