SOLUTION: 29.The Sum of the square of two numbers is 80 and the square of their difference is 36. The product of two numbers is

Question 912343: 29.The Sum of the square of two numbers is 80 and the square of their difference is 36. The product of two numbers is

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two numbers x & y
Write an equation for each statement
:
"The Sum of the square of two numbers is 80"
x^2 + y^2 = 80
" and the square of their difference is 36."
(x - y)^2 = 36
Foil (x-y)(x-y)
x^2 - 2xy + y^2 = 36
Use elimination, subtract from the 1st equation
x^2 + 0xy + y^2 = 80
x^2 - 2xy + y^2 = 36
------------------------Subtraction eliminates, both x^2 and y^2
2xy = 44
Divide both sides by 2
xy = 22
:
The product of two numbers is: 22
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