The difference between two numbers is 9, and the sum of the squares of each number is 153. What is the value of the product of the two numbers?

Logic
Sep 13, 2018

#2**+1 **

When you say " the sum of the squares of each number is 153", I take to mean "the sum of the squares of **both** numbers is 153". Based on that assumption, then we have:

x - y =9................................(1)

x^2 + y^2 = 153..................(2)

From (1) above: x =9 + y. sub this into (2) above:

(9 + y)^2 + y^2 = 153, solve for y

y^2 + 18y + 81 + y^2 =153

2y^2 + 18y + 81 - 153 = 0

2y^2 + 18y - 72 = 0 factor:

2(y - 3)(y + 12) = 0 divide both sides by 2

(y - 3)(y+ 12) = 0

y = 3 or y = -12 and:

x =12 or x =- 3

x*y =3*12 =36 or -3*-12 =36

Guest Sep 13, 2018