SOLUTION: How would you solve the following equation by factoring and applying the Zero-Product Property? {{{x^4-81=0}}}

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Question 165809: How would you solve the following equation by factoring and applying the Zero-Product Property?
x%5E4-81=0
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4-81 is the same thing as saying %28x%5E2%29%5E2-9%5E2 You may be familiar with the special rule for factoring "the difference of 2 perfect squares"
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The difference of two perfect squares is as follows:
a%5E2-b%5E2=%28a-b%29%28a%2Bb%29
this can be proven true by foiling (a-b)(a+b)=a%5E2%2Bab-ab-b%5E2=a%5E2-b%5E2
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So...in this equation
%28x%5E2%29%5E2-9%5E2=0
a=x%5E2 and b=9
so (x^2-9)(x^2+9)=0
the Zero-Product Property says that when 2 numbers are multiplied together, if either number is zero, then the product will be zero.
so
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the equation will be true when (x^2-9)=0 or when (x^2+9)=0
x%5E2-9=0
add 9 to each side
x%5E2=9
take the square root of each side
x=%2B-3
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x%5E2%2B9=0
Subtract 9 from each side
x%5E2=-9
take the square root of each side
x=SQRT%28-9%29 since we are unable to take the square root of a negative number, this is not a real solution.
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so
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The final answer is x=%2B-3 but the question is asking for all of the above work.
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