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.
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.
Let's assume that the three positive numbers are 3x, 4x, and 5x, where x is a positive constant.
According to the given ratio, the three numbers are in the ratio of 3:4:5.
Now, let's calculate the expression (product of the other two numbers) - (square of the middle number):
(3x * 5x) - (4x)^2 = 15x^2 - 16x^2 = -x^2
According to the problem, the result of this expression is equal to -x^2.
Since we know that the result is negative, we can conclude that x must be a positive number.
Therefore, the three numbers are 3x, 4x, and 5x, where x is a positive number.