Question 345201
(Note: The solution provided by another tutor is incorrect. The product of those answers is 30 and the square of the smaller number, 5, is 25. The product is 5 more than the square of the smaller number not 5 less than.)<br>
Let x = the smaller integer.
Then the next integer is x+1.
The product of these two integers is: {{{x(x+1) = x^2 +x}}}
The square of the smaller number is: {{{x^2}}}
The equation that says: "The product is 5 less than the square of the smaller number" is:
{{{x^2 + x = x^2 - 5}}}
To solve this we'll subtract {{{x^2}}} from each side:
{{{x = -5}}}
This is the smaller number. The next integer, x+1, is: -5 + 1 = -4
The two consecutive integers are: -5, -4<br>
Check:
The product of -5 and -4 is 20
The square of the smaller number, -5, is 25.
The product, 20, is indeed 5 less than 25, the square of the smaller number.