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

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Answer 1 · 2015-09-29T12:25:11

#color(blue)(x=+-3#

#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=(x^2)^2-(9^2)#

#=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.