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

solve the equation after making an appropriate substitution x^4-22x^2+96=0

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Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (277 lesson ratings) (277)
1

This equation factors.

x4 - 22x2 + 96=0

(x2 - 16)(x2 - 6) = 0

x2 = 16 or 6

x = ±4 or ±√6

Daniel O. | Math and Physics Tutor, with a math and physics degreeMath and Physics Tutor, with a math and ...
5.0 5.0 (265 lesson ratings) (265)
0

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.