Logs!!..But no wood..- part 2
If , then the value of
where x and y are coprime integers. Find the value of
The answer is 121.
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1 solution
a=(ab)^4...(1), b^4=a^-3, then simplify the equation by multiply 1/4 on the exponent of both side then plug in equation (1): b=a^-3/4=(ab)^-3...(2). After that, we can rewrite the number in the problem to: (a^1/3) (b^-1/2). Finally, we plug in equation (1) and (2) to get ((ab)^4/3) ((ab)^3/2)=(ab)^17/6. since x and y are co-prime integers, x=17, y=6. (x-y)^2=(17-6)^2=11^2=121.