SOLUTION: Chapter 10 Review Exercises #102 Find all real or imaginary solutionsto eah equation. Problem # 102 {{{ (w^2-1)^2+2(w^2-1)=15 }}}

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Question 80582This question is from textbook Elementary and Intermediate Algebra
: Chapter 10 Review Exercises #102
Find all real or imaginary solutionsto eah equation.
Problem # 102
+%28w%5E2-1%29%5E2%2B2%28w%5E2-1%29=15++
This question is from textbook Elementary and Intermediate Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(w^2-1)^2+2(w^2-1)=15
Let w^2-1= k
Then: k^2+2k-16=0
k=[-2+-sqrt(4-4*-16]/2
k=[-2+-2sqrt17]/2
k=-1+sqrt17 or k=-1-sqrt17
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Now solve for "w":
If w^2-1=-1+sqrt17
Then w^2=sqrt17
And w=+(17)^(1/4) or w=-(17)^(1/4)
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If w^2-1 = -1-sqrt17
Then w^2= -sqrt17
And w= +(17)^(1/4)i or w= -(17)^(1/4)i
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Cheers,
Stan H.