The sum of two numbers is 7 and the sum of their squares is 23, their product is equal to:
1). 10
2). 11
3). 12
4). 13
Let the two numbers be ‘x’ and ‘y’
Given x + y = 7 and x2 + y2 = 23
From the Algebraic Identity, we know that
(x + y)2 = x2 + y2 + 2xy
⇒ xy = [(x + y)2 - (x2 + y2)]/2 ----(1)
Substituting the values of (x + y) and (x2 + y2) in Equation 1, we get
⇒ xy = [(7)2 - 23]/2
⇒ xy = (49 - 23)/2 = (26/2) = 13
∴ Product of the numbers = 13