k(k-m)=12k(k+m)=60

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Well, you might not heard of this way but, yeah so...  I knew that 12 and 60 is a multiple of 6, and I also knew that 6*4=12 and 6*10=60. So then m has to be 4 and k has to be 6. And your answer is k = 6

You find what k is equal to...k(k-m)=12 to k=12/(k-m) by dividing both sides by k-mk(k+m)=12 to k=12/(k+m) by dividing both sides by k+m Then by the transitive property...12/(k-m)=12/(k+m)multiply both sides by  k+m  and divide both sides by 12 (which will cancel on both sides)(k-m)(k+m) = 1k^2-m^2=1  add both sides by m^2k^2=m^2+1 then square root both sidesk = plus or minus "m" plus or minus 1because taking the square root of a positive integer can result a positive or a negative. Squaring a negative integer will result as a positive number.