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

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) (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"

"is 37 less than the square of the largest number"

the equation can be set up as:

FOIL the left side:

subtract from both sides:

add 2 to both sides:

divide both sides by -3:

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

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