SOLUTION: The sum of 2 numbers is 10 and the product of the same two numbers is 20. What is the sum of the square of the two numbers? I know the answer is 60 but i don't know what equatio

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Question 449134: The sum of 2 numbers is 10 and the product of the same two numbers is 20. What is the sum of the square of the two numbers?
I know the answer is 60 but i don't know what equation to use to find that. (I used a calculator)
Found 2 solutions by stanbon, rwm:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of 2 numbers is 10 and the product of the same two numbers is 20. What is the sum of the square of the two numbers?
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Equations:
x + y = 10
xy = 20
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Substitute for "y" and solve for "x":
x(10-x) = 20
-x^2+10x-20 = 0
----
x^2-10x+20 = 0
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x = [10 +- sqrt(100-4*20)]/2
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x = [10 +- sqrt(20)]/2
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x = [5 +- sqrt(5)]
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x = 5+sqrt(5) or x = 5-sqrt(5)
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If x = 5+sqrt(5), y = 2.7639
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If x = 5-sqrt(5), y = 7.2361
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C10-x%2C20%2Fx%29
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Cheers,
Stan H.

Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
a+b=10
a*b=20