SOLUTION: {{{x^4}}}+1={{{6x^2}}}

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Question 61784: x%5E4+1=6x%5E2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+%2B+1+=+6x%5E2
x%5E4+-+6x%5E2+%2B+1+=+0
solve by completing the square
If b is the coefficient of x%5E2,
then x%5E4+-+bx%5E2+%2B+%28b%2F2%29%5E2+=+0
First subtract 1 from both sides
x%5E4+-+6x%5E2+=+-1
x%5E4+-+6x%5E2+%2B+9+=+-+1+%2B+9
%28x%5E2+-+3%29%5E2+=+8
take the square root of both sides
x%5E2+-+3+=+2%2A%280%2B-sqrt%282%29%29
x%5E2+=+3+%2B+2sqrt%282%29 and
x%5E2+=+3+-+2sqrt%282%29
solving for x
x+=+%2B+sqrt%283+%2B+2sqrt%282%29%29
x+=+-+sqrt%283+%2B+2sqrt%282%29%29
x+=+%2B+sqrt%283+-+2sqrt%282%29%29
x+=+-+sqrt%283+-+2sqrt%282%29%29
Try each of these. I tried one, and
it was a solution