# How do you solve x^4-81=0?

Sep 29, 2015

color(blue)(x=+-3

#### Explanation:

${x}^{4} - 81 = 0$

By property
color(blue)(a^2-b^2=(a-b)(a+b)

Similarly we can rewrite the expression given :

${x}^{4} - 81 = {\left({x}^{2}\right)}^{2} - \left({9}^{2}\right)$

=color(blue)((x^2-9)(x^2+9)

Equating the factors to zero:

1) ${x}^{2} - 9 = 0$
${x}^{2} = 9$
color(blue)(x=+-3

2) ${x}^{2} + 9 = 0$
${x}^{2} = - 9$
This case is not applicable as we cannot take the root of a negative number.