SOLUTION: Find two consecutive numbers such that the sum of their squares is 35 more than twice the square of the smaller.

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Question 54440: Find two consecutive numbers such that the sum of their squares is 35 more than twice the square of the smaller.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this:
Let x be the smaller number, then x+1 will be the next consecutive number.
x%5E2+%2B+%28x%2B1%29%5E2+=+2x%5E2%2B35 Simplify and solve for x.
x%5E2+%2B+%28x%5E2%2B2x%2B1%29+=+2x%5E2%2B35
2x%5E2%2B2x%2B1+=+2x%5E2%2B35 Subtract 2x^2 from both sides.
2x%2B1+=+35 Subtract 1 from both sides.
2x+=+34 Finally, divide both sides by 2.
x+=+17 and x%2B1+=+18
Check:
17%5E2+%2B+18%5E2+=+289+%2B+324 = 613
2%2817%5E2%29+%2B+35+=+578+%2B+35 = 613