what is up with these quad. equations?

[Molly]

If anyone can help me with this problem it would be greatly appreciated....

Find three consecuative positive odd intagers such that the sum of the squares of the first two are 15 less than than the square of the third??????? I have to compleate that with a quad equation????? please help>>>>>.Thanks

 

[TchrWill]

If anyone can help me with this problem it would be greatly appreciated....

Find three consecuative positive odd intagers such that the sum of the squares of the first two are 15 less than than the square of the third??????? I have to compleate that with a quad equation????? please help>>>>>.Thanks

Let the three number be x, (x + 2) and (x + 4).

Then x^2 + (x + 2)^2 = (x + 4)^2 - 15.

Expand, simplify, and you will have your quadratic.

 

[pka]

\(\displaystyle \L
\left( {2k + 1} \right)^2 + \left( {2k + 3} \right)^2 + 15 = \left( {2k + 5} \right)^2\)

 

[jacket81]

Well, with it being consecutive odd numbers, then that means there's a difference of 2 between the consecutive numbers.

SO, x^2+(x+2)^2 = (x+4)^2-15.

So, x^2+x^2+4x+4 = x^2+8x+16-15.

ANd arranging the equation such that the right side equals 0,
x^2-4x+3 = 0.

ANd you can factor this to (x-1)(x-3)=0.

SO, x=1, and x=3.

So, that gives you 1,3,5 and 3,5,7.