What two numbers when multiplied together equal 60 and when added equal 22?

Answer 1

82

Answer 2

Let the first number be x, so the other will be 22 - x. So we have:

x(22 - x) = 60

-x2 + 22x = 60

-(x2 - 22x) = 60

x2 - 22x = -60

x2 - 22x + 112= 112 - 60

(x - 11)2 = 61

x - 11 = ±√61

x = 11 ± √61

x = 11 + √61 or x = 11 - √61

if x = 11 + √61, the other number is 11 - √61 because 22 - (11 + √61) = 22 - 11 - √61

if x = 11 - √61, the other number is 11 + √61 because 22 - (11 - √61) = 22 - 11 + √61