edwinsummerour2 edwinsummerour2
  • 18-06-2018
  • Mathematics
contestada

What substitution should be used to rewrite 4x^4-21x^2+20=0

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sqdancefan
sqdancefan sqdancefan
  • 19-06-2018
You can use z = x², then rewrite the equation as
  4z²-21z+20 = 0
This factors as
  (4z-5)(z-4) = 0
so has solutions
  z = 5/4, 4

The solutions for x are then
  x = ±√z = {-2, -(√5)/2, (√5)/2, 2}
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