Three positive numbers are in the ratio of 3:4:5. When the square of the middle is subtracted from the product of the other two numbers, the answer is- find the numbers.

Answer 1

Let the three numbers be $3x, 4x, 5x$. We have $(3x)(5x)-(4x)^2=15x^2-16x^2=-x^2=-1\implies x=1$. Thus, the three numbers are $3,4,5$, respectively.