The product of 2 consecutive even numbers is 12 more than the square of the smaller number. Find the numbers?

Posted on June 8, 2010 by admin

The product of 2 consecutive even numbers is 12 more than the square of the smaller number. Find the numbers?

Let the first consecutive number be x. It then follows that the second consecutive number must be x + 2.

"The product of 2 consecutive even numbers …."
(product means multiply)

x(x + 2)

"is"

=

"12 more"

+ 12

"than the square of the smaller number"
x^2

Put it all together, and you get

x(x + 2) = x^2 + 12

Just solve for x.

x^2 + 2x = x^2 = 12

Subtract x^2 both sides, to get

2x = 12
x = 6

That makes the first number x = 6, which means the second number is 8.

The numbers are 6 and 8.

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9 Responses to The product of 2 consecutive even numbers is 12 more than the square of the smaller number. Find the numbers?

  1. Puggy says:
    June 9, 2010 at 1:55 am

    Let the first consecutive number be x. It then follows that the second consecutive number must be x + 2.

    "The product of 2 consecutive even numbers …."
    (product means multiply)

    x(x + 2)

    "is"

    =

    "12 more"

    + 12

    "than the square of the smaller number"
    x^2

    Put it all together, and you get

    x(x + 2) = x^2 + 12

    Just solve for x.

    x^2 + 2x = x^2 = 12

    Subtract x^2 both sides, to get

    2x = 12
    x = 6

    That makes the first number x = 6, which means the second number is 8.

    The numbers are 6 and 8.
    References :

  2. norman says:
    June 9, 2010 at 2:02 am

    (n+2)n – n^2 = 12
    n^2 + 2n – n^2 = 12
    2n = 12
    n = 6

    6×8 = 48 6×6 = 36 48-36=12
    References :

  3. mindmeme2012 says:
    June 9, 2010 at 2:41 am

    6 and 8
    References :

  4. smpel says:
    June 9, 2010 at 2:46 am

    x.(x+2)=x^2+12 =>
    x^2+2x=x^2+12 =>
    2x=12 => x=6
    y=8
    References :

  5. Nur S says:
    June 9, 2010 at 3:04 am

    x(x+2) -12 = x^2

    x^2 + 2x – 12 = x^2

    x1=6 , x2 = 8
    References :

  6. D Rocker says:
    June 9, 2010 at 3:27 am

    x(x+2) = x^2 + 12

    x^2 + 2x = x^2 + 12
    (x^2 cancels)

    2x = 12

    x =6

    the numbers are 6 and 8

    6X8 = 48
    6^2 = 36
    References :

  7. Blue Sky says:
    June 9, 2010 at 3:54 am

    X (X + 2) – 12 = X^2

    X^2 + 2X – 12 = X^2

    2X = 12

    X = 6
    X + 2 = 8
    References :

  8. D.W. says:
    June 9, 2010 at 4:34 am

    "2 consecutive even numbers"
    2x and 2(x+1)

    "The product is 12 more than the square of the smaller"
    (2x)2(x+1) = 12 + (2x)²

    Solve for x:
    4x² + 4x = 12 + 4x²
    4x = 12
    x = 3
    2x=6
    2(x+1) = 8
    the numbers are 6 and 8
    References :

  9. ames812 says:
    June 9, 2010 at 5:11 am

    Set up an equation.

    The product of two consecutive numbers can be written as n * (n+2) ((We say n + 2 since the next even number is two more than the one we have))

    The square of the smaller number can be written as n^2
    Our equation:
    n * (n + 2) -12 = n^2

    Now we get rid of the parenthesis
    n^2 + 2n – 12 = n^2

    Subtract n^2 from both sides
    2n – 12 = 0

    Add 12 to both sides
    2n = 12

    Divide by 2
    n = 6

    The smaller number must be 6 and the larger number must be 8

    6 * 8 = 48
    6^2 = 36

    6*8 is 12 bigger than 6^2
    References :