Two numbers sum is 13 and their product is 42 Find these two

Two numbers’ sum is -13, and their product is 42. Find these two numbers.

These two numbers are ___________ . (Use a comma to separate your numbers.)

Solution

Let the numbers be x and y. Then x + y = -13 ..(1) and xy = 42..(2). From the 1st equation, we have y = - (x + 13). On substituting y = -(x + 13) in the 2nd equation, we have - x ( x + 13) = 42 or, x ²+ 13x+ 42 = 0.or, x² + 6x +7x + 42 = 0 or x(x + 6) + 7 (x + 6) = 0 or, (x+ 6)(x + 7) = 0 Therefore, either x = -6 0r -7. When x = -6, y = -(x + 13) = -18.358)/2 = -31.358/2 = -15.679. Therefore, y = - (x + 13) = -7 and when x = -7, y =  - (x + 13) = - 6. Thus, the required numbers are -6 and -7.or -6, -7.