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

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18-06-2018
Mathematics

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

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sqdancefan sqdancefan · Answer 1 · 2018-06-19T18:43:53+02:00

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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