Glitch Glitch
  • 04-08-2024
  • Mathematics
Middle School

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

Answer :

sqdancefan sqdancefan
  • 31-08-2023
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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