SOLUTION: Find three consecutive even integers such that the square of the first is 80 less than the square of the third. (Only an algebraic solution will be accepted. )

Question 1102792: Find three consecutive even integers such that the square of the first is 80 less than the square of the third. (Only an algebraic solution will be accepted. )
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let n be the central of these tree consecutive integers, so that the numbers are

n-2, n and n+2.


Then the condition says

(n+2)^2 - (n-2)^2 = 80,   or, expanding parentheses,

n^2 + 4n + 4 - (n^2 -4n +4) = 80,

which is simplified to

8n = 80.


Hence, n =  = 10.


Answer.  The numbers are 8, 10 and 12.


Check.   12^2 - 8^2 = 144 - 64 = 80.   ! Correct !

Solved.

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