SOLUTION: x4 + 2x2 – 1 = 0

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Question 175567: x4 + 2x2 – 1 = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+%2B+2x%5E2-1+=+0
You can use a substitution and knock this down to a quadratic equation.
Let z=x%5E2
x%5E4%2B2x%5E2-1=0
z%5E2%2B2z-1=0
Use the quadratic formula,
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
z+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29%29%29%2F%282%2A1%29+
z+=+%28-2+%2B-+sqrt%28+4%2B4%29%29%2F%282%29+
z+=+-1+%2B-+sqrt%282%29
Two solutions for z.
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First solution for z,
z+=+-1+%2B+sqrt%282%29
x%5E2+=+-1+%2B+sqrt%282%29
Two real roots,
x+=0+%2B-+sqrt%28-1+%2B+sqrt%282%29%29
or approximately
x=0.643 and x=-0.643
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Second solution for z,
z+=+-1+-+sqrt%282%29
x%5E2=+-1+-+sqrt%282%29
Two complex roots,
x%5E2=+%28-1%29%2A%281%2Bsqrt%282%29%29
x=+0+%2B-+sqrt%28%28-1%29%2A%281%2Bsqrt%282%29%29%29
x=+0+%2B-+sqrt%281%2Bsqrt%282%29%29i
or approximately
x=1.554i and x=-1.554i
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The graph verifies the real roots.
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+graph%28+300%2C+300%2C+-2%2C+2%2C+-10%2C+10%2C+x%5E4%2B2x%5E2-1%29+