But that would be 5!

Algebra Level 3

If the following equation

x 2 − 240 x + 14400 x 2 − 5 x + 6 = 0 \large \frac{x^{2} - 240x + 14400}{x^{2} - 5x + 6} = 0

has one solution that can be written in the form of a b \frac{a}{b} where a a and b b are co-prime. Find a − b a - b .


The answer is 119.

Evan Huynh by Evan Huynh , 24, Sweden

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1 solution

Kay Xspre
Jan 6, 2016

If quickly noticed, x 2 − 240 x + 14400 x^2-240x+14400 is ( x − 120 ) 2 (x-120)^2 , hence the answer is 120 (which is valid as 120 ≠ 2 , 3 120 \neq 2, 3 ). The a − b a-b is then 120 − 1 = 119 120-1 = 119

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