Chapter ISG, Problem 8.7.2.2P

To determine

To verify statement

Answer to Problem 8.7.2.2P

Statement is correct.

Explanation of Solution

Given information:

  $y=x^4-81$

Calculation:

Using identity $a^2-b^2=(a+b)(a-b)$ ,

  $x^4-81$ Can be written as $(x^2-9)(x^2+9)$

Also,

  $(x^2-9)$ can be written as $(x+3)(x-3)$ ,

So using identity twice,

  $y=x^4-81$ , put this equal 0 to factorise.

  $x^2-81=$ 0

  $(x^2+9)(x+3)(x-3)=0$

Zeroes are 3, -3 and $\pm \sqrt{9}$

Zeroes of $(x^2-9)$ are $\pm \sqrt{9}$ which are also 3, -3.

Hence, statement is correct