SOLUTION: Type an exact answer using radicals as needed and use commas to separate answers. What is the solution? w = w^4 - 2w^2 - 2 = 0

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Question 319350: Type an exact answer using radicals as needed and use commas to separate answers. What is the solution? w =
w^4 - 2w^2 - 2 = 0
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
w^4 - 2w^2 - 2 = 0
:
Find w^2 using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this equation
x=w^2, a=1, b=-2, c=-2
w%5E2+=+%28-%28-2%29+%2B-+sqrt%28-2%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29+
:
w%5E2+=+%282+%2B-+sqrt%284+-+%28-8%29+%29%29%2F2+
:
Two solutions
w%5E2+=+%282+%2B+sqrt%2812+%29%29%2F2+
w%5E2+=+%282+%2B+sqrt%284%2A3%29%29%2F2+
extract the sqrt of 4
w%5E2+=+%282+%2B+2%2Asqrt%283%29%29%2F2+
Cancel the 2's
w%5E2+=+1+%2B+sqrt%283%29+
Find the square root of both sides
w = sqrt%281%2Bsqrt%283%29%29; a good solution
:
but we also have
w%5E2+=+%282+-+sqrt%2812+%29%29%2F2+
w%5E2+=+%282+-+sqrt%284%2A3%29%29%2F2+
extract the sqrt of 4
w%5E2+=+%282+-+2%2Asqrt%283%29%29%2F2+
Cancel the 2's
w%5E2+=+1+-+sqrt%283%29+
Find the square root of both sides
w = sqrt%281-sqrt%283%29%29
However sqrt of 3 > 1, therefore we have square root of a neg number
:
I'm going to say the exact solution using radicals
w = +sqrt%281%2Bsqrt%283%29%29, -sqrt%281%2Bsqrt%283%29%29
:
Confirm this with a graph of this equation
+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+4%2C+x%5E4-2x%5E2-2%29+