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x^4-22x^2+96=0

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2 Answers

You could make a substitution u = x2

You can rewrite x4 - 22x2 + 96 = 0 as

(x2)2 - 22(x2) + 96 = 0 which makes it easier to see where to make the substitution:

u2 - 22u + 96 = 0

now factor it by finding two numbers which multiply to equal 96, and add up to -22: (-6)*(-16) = 96 and (-6) + (-16) = -22

(u - 16)(u - 6) = 0

u = 16 or u = 6. Remember that u = x2 and now you can solve it as Roman did.

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