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Phoenix [80]
3 years ago
6

What is the solution to x4 - 12x2+10>0

Mathematics
1 answer:
alexira [117]3 years ago
5 0

Answer:

  (-√(6-√26) < x < √(6-√26)) ∪ (x < -√(6 +√26)) ∪ (√(6 +√26) < x)

Step-by-step explanation:

Using x^2 = z, the equation can be rewritten as ...

  z^2 -12z +10 > 0

  (z -6)^2 -26 > 0

  |z -6| > √26

This resolves to two equations.

This one ...

  x^2 -6 < -√26 . . . . substitute x^2 for z

  |x| < √(6-√26) . . . . add 6, take the square root; use √a^2 = |a|

  -√(6-√26) < x < √(6-√26)

__

and this one ...

  x^2 -6 > √26

  |x| > √(6 +√26)

  x < -√(6 +√26) ∪ √(6 +√26) < x

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