The difference between two numbers is 1, and the sum of their squares is 141. What is the product of the numbers?

Answer 1

x^2 + y^2 = 141

x-y = 1

y=x-1

x^2 + (x-1)^2 = 141

x^2 + x^2 -2x +1 = 141

2x^2 -2x = 140

x^2 -x -70 = 0

x = 1/2 + or - (1/2)sqr(1+280) = about 17.76/2 or -15.76/2

x = 8.88 or -7.88

y= 7.88 or -8.88

xy = about 70

8.88^2 + 7.88^2 = about 79 + 62 = 141

actually the product is exactly 70

(.5 + .5sqr281)(-.5+.5sqr281) = .25(281 -.25 = 70.25 - .25 = 70