Two numbers differ by 5. If their product is 336, the sum of the two numbers is:____________?21283751

Let's denote the two numbers as x and y.

From the problem, we know that:

1. x - y = 5 (the two numbers differ by 5)
2. xy = 336 (their product is 336)

We need to find x + y.

First, we can express y in terms of x using the first equation: y = x - 5.

Substitute y in the second equation: x(x - 5) = 336.

This simplifies to: x^2 - 5x - 336 = 0.

This is a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -5, and c = -336.

We can solve this equation using the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Substituting the values of a, b, and c into the formula gives: x = [5 ± sqrt((-5)^2 - 41(-336))] / (2*1).

Solving this gives two possible values for x: 21 and -16.

Since x and y are numbers that differ by 5, x cannot be -16. So, x = 21.

Substitute x = 21 into the equation y = x - 5 to find y. This gives y = 21 - 5 = 16.

Finally, the sum of the two numbers is x + y = 21 + 16 = 37.