Question

The sum of two numbers is 17, and the sum of their squares is 145. What is the product of the numbers?

Answer 1

72

Explanation:

let the numbers be x&y

1.x+y=17

2.x²+y²=145

3.xy=?

x²+y² can't be factorised

but (x+y)²=x²+2xy+y²

(x+y)²=x²+y²+2xy

(x+y)²-2xy=x²+y²

(17)²-2(xy)=145

289-2(xy)=145

-2(xy)=145-289

-2(xy)=-144

-2(xy)/-2=-144/-2

xy=72