SOLUTION: Sum of the squares of two numbers is 100. Sum of the numbers is 2. Find the numbers.

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Question 432719: Sum of the squares of two numbers is 100. Sum of the numbers is 2. Find the numbers.
Found 2 solutions by edjones, Gersid:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+y^2=100
x+y=2
y=2-x
x^2+(2-x)^2=100
x^2+4-4x+x^2=100
2x^2-4x-96=0
x^2-2x-48=0
(x-8)(x+6)=0
x=8, y=-6
.
Ed

Answer by Gersid(33) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be m and n.
1) m%5E2%2Bn%5E2+=+100 "The sum of the squares of two numbers is 100."
2) m+%2B+n+=+2 "The sum of the numbers is 2." Rewrite this as m+=+2-n and substitute for m in equation 1).
1a) %282-n%29%5E2%2Bn%5E2+=+100 Simplify.
2b) 4-4n%2Bn%5E2%2Bn%5E2+=+100
2c) 2n%5E2-4n%2B4+=+100 Subtract 100 from both sides.
2d) 2n%5E2-4n-96+=+0 Solve by factoring.
2e) 2%28n%5E2-2n-48%29+=+0
2f) 2%28n%2B6%29%28n-8%29+=+0
2g) n%2B6+=+0 or n-8+=+0
So, n+=+-6 or n+=+8
The two numbers are -6 and 8.