SOLUTION: "The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 160. Find the larger even integer."

Question 1043101: "The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 160. Find the larger even integer."
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
2n and 2n+2

The hard part was to formulate that equation.

Solving for n is arithmetic according to the rules about numbers you have been studying (algebra, number properties, quadratic equations).
Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!

"The square of the sum of two consecutive positive even integers is greater than the sum of their squares by 160. Find the larger even integer."

Let the larger integer be L
Then smaller is: L - 2
We then get:

Factor this trinomial, set each factor equal to 0, and then obtain the value(s) for L, the larger integer.
Ignore the negative value, as L, or larger integer should be positive (> 0).
RELATED QUESTIONS
The square of the sum of two consecutive positive even integers is greater than the sum... (answered by CubeyThePenguin)
the sum of the squares of two consecutive positive even integers is 340. find the... (answered by HyperBrain)
the sum of the squares of two consecutive positive even integers is 340. find the... (answered by bucky)
The sum of the squares of two consecutive even positive integers is 340.Find the... (answered by checkley77)
the sum of the squares of two positive consecutive even integers is 100. Find the... (answered by drk)
the sum of the squares of two consecutive positive even integers is 340. Find the... (answered by harpazo)
TWO CONSECUTIVE POSITIVE EVEN INTEGERS ARE SUCH THE SUM OF THEIR SQUARES IS 164. FIND... (answered by mananth)
Find three consecutive positive even integers such that the sum of their squares is... (answered by Alan3354)
find two consecutive positive even numbers such that the sum of their squares is 164. (answered by Alan3354)