SOLUTION: there are 3 consecutive positive odd integers. the difference between the squares of the largest and smallest is 9 less than the square of the middle integer. use a complete al

Question 679675:
there are 3 consecutive positive odd integers. the difference between the squares of the largest and smallest is 9 less than the square of the middle integer. use a complete algebraic solution to find the integer
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
LET X, X+2 & X+4 BE THE 3 INTEGERS.
(X+4)^2-X^2=(X+2)^2-9
X^2+8X+16-X^2=X^2+4X+4-9
8X+16=X^2+4X-5
X^2+4X-8X-5-16=0
X^2-4X-21=0
(X-7)(X+3)=0
X-7=0
X=7 ANS.
7+2=9 ANS.
7+4=11 ANS.
PROOF:
11^2-7^2=9^2-9
121-49=81-9
72=72

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