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

Answer 1

Julia Adams

#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.

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Answer 2

Jameson Allen

To solve (x^4 - 81 = 0), you can follow these steps:

Add 81 to both sides of the equation: (x^4 = 81)
Take the fourth root of both sides: (x = \pm \sqrt[4]{81})
Simplify the fourth root of 81: (x = \pm \sqrt[4]{3^4})
Since (\sqrt[4]{3^4}) equals 3, the solutions are: (x = \pm 3)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.