SOLUTION: The sum of two numbers is 14 and the sum of their sqaures is 100. What are the numbers

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Question 1045481: The sum of two numbers is 14 and the sum of their sqaures is 100. What are the numbers
Found 2 solutions by jhunjiro, josgarithmetic:
Answer by jhunjiro(67) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
x= 1st number
y= 2nd number
The sum of two numbers is 14 means x%2By=14 eq 1
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the sum of their sqaures is 100 means x%5E2%2By%5E2=100 eq2
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solve for y in eq 1 then substitute to eq 2
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y=14-x
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x%5E2%2B%2814-x%29%5E2=100 then simplify
x%5E2%2B%28196-28x%2Bx%5E2%29=100
2x%5E2%2B196-28x=100
2x%5E2%2B196-28x-100=0
2x%5E2-28x%2B96=0
use quadratic formula to get the value of x. either of the two values can satisfy the problem so choose any.
a=2
b=-28
c=96
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=6
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y=14-6
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y=8
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The two numbers are 6 and 8.

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=14%2Cx%5E2%2By%5E2=100%29

x%5E2%2B%2814-x%29%5E2=100
x%5E2%2B196-28x%2Bx%5E2-100=0
2x%5E2-28x%2B96=0
x%5E2-14x%2B48=0
%28x-6%29%28x-8%29=0

The two numbers are 6 and 8.