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The sum of two numbers is 7 and the sum of their squares is 23, their product is equal to: 

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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


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Answered by on | Votes 3 |

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

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