Question 277116
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"
{{{(x-2)(x-1)}}}
"is 37 less than the square of the largest number"
{{{x^2-37}}}
the equation can be set up as:
{{{(x-2)(x-1)=x^2-37}}}
FOIL the left side:
{{{x^2-3x+2=x^2-37}}}
subtract {{{x^2}}} from both sides:
{{{-3x+2=-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