SOLUTION: The difference of two positive numbers is 1 and the sum of their squares is 61. Find the numbers.

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Question 658159: The difference of two positive numbers is 1 and the sum of their squares is 61. Find the numbers.
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be x and x+1
x%5E2+%2B+%28x%2B1%29%5E2+=+61
x%5E2+%2B+%28x%5E2+%2B+2x+%2B+1%29+=+61
2x%5E2+%2B+2x+-+60+=+0
x%5E2+%2B+x+-+30+=+0
We can solve for x using the quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ with a=1, b=1, and c=-30:
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-30%29+%29%29%2F%282%2A1%29+
x+=+%28-1+%2B-+sqrt%28+1-%28-120%29+%29%29%2F2+
x+=+%28-1+%2B-+sqrt%28+121+%29%29%2F2+
x+=+%28-1+%2B-+11%29%2F2+
And since we're only looking for positive integers:
x+=+%28-1+%2B+11%29%2F2+
x+=+10%2F2+=+5+
So the two numbers are 5 and 6