SOLUTION: whats the answers to this question . the sum of two integers is 7,and the sum of their squares is 25. what is the product of these two integers

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Question 941236: whats the answers to this question . the sum of two integers is 7,and the sum of their squares is 25. what is the product of these two integers
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
x + y = 7
x^2 + y^2 = 25

Rearrange to get y = 7 - x.

x^2 + (7 - x)^2 = 25
x^2 + (49 - 14x + x^2) = 25
2x^2 - 14x + 24 = 0
x^2 - 7x + 12 = 0
(x - 3)(x - 4) = 0

x = 3 or 4
y = 4 or 3

Answer by ikleyn(52811) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given


    x   + y   =  7       (1)

    x^2 + y^2 = 25.      (2)


Square the first equation. You will get


    x^2 + 2xy + y^2 = 49.


Subtract equation (2) from it.  You will get


    2xy = 49 - 25 = 24.


It implies


    xy = 24/2 = 12,


which is your answer.

Solved.