Easy one for olympiad aspirators

If 4x-y is divisible by 3, prove that 4x2+7xy-2y2 is divisible by 9.

3 Answers

341
Hari Shankar ·

Not related but aspirators is not the word you are looking for. Since I have some link to the medical field, I am familiar with http://en.wikipedia.org/wiki/Aspirator

Should be aspirants

1
Che ·

4x-y=3m

y=4x-3m

put y=4x-3m in 4x2+7xy-2y2

u will get 4x2+7xy-2y2 as 9m(3x-2m)

hence divisible by 9

341
Hari Shankar ·

4x2+7xy-2y2=(4x-y)(x+2y)

So we only need to prove that x+2y = (4x-y)-3(x-y) is divisible by 3 which is obvious.

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