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Algebra Level pending

Find the sum of all values of x x [ 2 x x − 5 ] 2 + [ 10 x x − 5 ] − 24 = 0 [\frac{2x}{x-5}]^2+[\frac{10x}{x-5}]-24=0 .


The answer is 19.

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1 solution

Chan Lye Lee
Nov 3, 2015

Let u = 2 x x − 5 u=\frac{2x}{x-5} . Then the original equation becomes u 2 − 5 u − 24 = 0 u^2-5u-24=0

This means that u = − 8 u=-8 or u = 3 u=3 . Now x = 4 x=4 and x = 15 x=15 respectively.

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