SOLUTION: I need help find three consecutive odd integers whose squrares have a sum of 155 can you help me?

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Question 287723: I need help find three consecutive odd integers whose squrares have a sum of 155 can you help me?
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the first odd integer. Since every odd integer is 2 larger than the previous one, the next odd integer must be and the one after that,

The square of the first one is:

The square of the second one is:

The square of the third one is:

The sum of the squares, after collecting like terms (verification left as an exercise for the student) is:

And this sum is equal to 155:

Factor and solve the quadratic. Quadratics have two solutions. Check both of them to see if they both satisfy the conditions of the problem.

John

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
155/3 = almost 52
sqrt(52) = apx 7, the middle number
--> 5, 7, 9
and -9, -7, -5