What two numbers multiply to be 135 and add to be 42?

Answer 1

177

Answer 2

Let the numbers be x and y. So we have,

xy = 135

x + y = 42, which yield y = 42 - x (use substitution method to solve the linear system of the equations)

xy = 135 (substitute y by 42 - x)

x(42 - x) = 135

42x - x2 = 135 (subtract 135 to both sides)

42x - x2 - 135 = 0 (multiply by -1 to both sides)

x2 - 42x + 135 = 0 (use the quadratic formula to solve for x)

x = [-(-42) ± √[422 - 4(1)(135)]]/2(1)

x = [42 ± √(1,764 - 540)]/2

x = (42 ± √1,224)/2

x = 42/2 ± (√1,224)/2

x = 21 ± √1,224/4 = 21 ± √306

x ≈ 21 ± 17.5

x ≈ 21 + 17.5 or x ≈ 21 - 17.5

x ≈ 38.5 or x ≈ 3.5

y = 42 - x (replace x with 38.5 or 3.5)

y = 42 - 38.5 = 3.5, so that

y = 3.5 or y = 38.5

Thus, the numbers are approximately to 38.5 and 3.5