SOLUTION: Find 3 consecutive numbers where the product of the smaller two numbers is 37 less than the square of the largest number.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find 3 consecutive numbers where the product of the smaller two numbers is 37 less than the square of the largest number.      Log On


   

Question 202163: Find 3 consecutive numbers where the product of the smaller two numbers is 37 less than the square of the largest number.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
We'll assume they mean three consecutive integers.
Let x be the smallest. Then the other two numbers are x%2B1 and x%2B2
Given
x%2A%28x%2B1%29+=+%28x%2B2%29%5E2+-+37
x%5E2+%2B+x+=+x%5E2+%2B+4x+%2B+4+-+37
x+=+4x+-+33
-3x+=+-33
x+=+11
So the numbers are 11, 12 and 13.
Check your answer:
Does 11*12 = 13^2 - 37???