Algebra integers

Question

The product of two consecutive integers is the square of the lesser integer minus 5. Find the greater of the two integers.

Answer 1

Hi Anthony, if we let x be the first of the two consecutive integers, then the second of the two consecutive integers becomes x + 1.  The equation becomes:

 

x(x + 1) = x^2 - 5

 

Clear the parenthesis giving:

 

x^2 + x = x^2 - 5

 

Subtract x^2 from both sides giving:

 

x = -5, or the smaller of the two consecutive integers.

 

The larger of the two consecutive integers is x+1 or -5 + 1, which equals -4.  

 

Remember, smaller numbers move to the left on the number line and -5 is smaller than -4.

 

To check, substitute for x in the original equation giving:

 

-5(-4 + 1) = (-5)^2 - 5

 

-5 * -4 = 25 - 5

 

20 = 20

 

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