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

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Question 277116: Find 3 consecutive numbers where the product of the smaller two numbers is 37 less than the square of the largest number.
Answer by muffin8(5) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the highest number.
The numbers are consecutive so they are 1 away from each other.
The 3 numbers can be represented as:
x (the highest number)
x-1 (the next number below x)
x-2 (the second next number below x)
The problem says:
"the product of the smaller two numbers"
%28x-2%29%28x-1%29
"is 37 less than the square of the largest number"
x%5E2-37
the equation can be set up as:
%28x-2%29%28x-1%29=x%5E2-37
FOIL the left side:
x%5E2-3x%2B2=x%5E2-37
subtract x%5E2 from both sides:
-3x%2B2=-37
add 2 to both sides:
-3x=-39
divide both sides by -3:
x=-13
The numbers are 13,12 and 11.
Check your answer:
"product of the smaller two numbers"
11*12 = 132
"is 37 less than the square of the largest number"
13*13-37 = 132