A very nice math olympiad problem

In this video, I'll be showing you step by step on how to solve this olympiad Algebra problem using a simple trick.

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[davidellis]

Here's a similar solution: Let a=xb. Then b+xb=6b*sqrt(x). Since we are looking for a/b, b can't be zero. Dividing both sides by b yields 1+x=6*sqrt(x). Square both sides: x^2+2x+1=36x, so
x^2-34x+1=0. Complete the square: (x-17)^2=x^2-34x+17^2=288=(12*sqrt(2))^2, yielding
a/b=x=(17 plus or minus 12*sqrt(2)).

[JosephPedis]

How to solve simultaneous equations apart from elimination and substitution methods