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?
Answer by MRperkins(300) (Show Source): You can put this solution on YOUR website!
is the same thing as saying 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:
this can be proven true by foiling (a-b)(a+b)==
.
So...in this equation
and
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
.
the equation will be true when (x^2-9)=0 or when (x^2+9)=0
add 9 to each side
take the square root of each side
.
Subtract 9 from each side
take the square root of each side
since we are unable to take the square root of a negative number, this is not a real solution.
.
so
.
The final answer is but the question is asking for all of the above work.
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