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[sungkwo]

If a^2b^3=1323 and a and b are integers, find the values of a and b. The answers are a=7 and b=3. Is there anyway to solve this question without 'guessing and checking'?

 

[vds700]

If a^2b^3=1323 and a and b are integers, find the values of a and b. The answers are a=7 and b=3. Is there anyway to solve this question without 'guessing and checking'?

i dont think its possible to solve an equation with 2 variables, unless you had another equation, so you could solve them simultaneously....could be wrong though.

I think, as you said, guessing and checking i the only way, as they specify a and b are integers

 

[DownInFlames]

a^2 * b^3 = 1323
= 27 * 49
=3^3 * 7^2

by equating the two, a=7 and b=3

I got this by knowing I needed a cube and a square, so I guess I technically trial and error-ed it. Sometimes you can do this in math, you just need to know what to look for, and that it can't possibly be too big a number in this question.

Here I would look at the cubes of numbers first, 1323 by each and see which one gives you a perfect square as well.