Chapter 9.4, Problem 61HP

To determine

Find the solution.

Answer to Problem 61HP

  $x=\pm 3$

Explanation of Solution

Given Information: $x^4-18x^2+81=0$

Formula Used: $a^2+2ab+b^2={(a+b)}^2$ and $a^2-b^2=(a+b)(a-b)$

Calculation:

  $x^4-18x^2+81=0$

So, simplify

  $x^4-9x^2-9x^2+81=0$

Now,

  $x^2\left(x^2-9\right)-9\left(x^2-9\right)=0$

Now,

  $\left(x^2-9\right)\left(x^2-9\right)=0$

Now,

  $\left(x^2-9\right)=0$

So,

  $x^2=9$

Now, square root both sides

  $x=\sqrt{9}$

Hence,

  $x=\pm 3$