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The sum of the squares of two consecutive positive odd numbers is 650.  Find the numbers.

 Feb 27, 2021
 #1
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integers are (x) and (x+2)

 

 

\(x^2 + (x+2)^2 = 650\)

 

\(2x^2 +4x + 4 = 650\)

 

\(x^2 + 2x - 323 = 0\)

 

\((x+19)(x-17) = 0\)

 

The integers are positive, so x = 17.

 

The numbers are 17 and 19.

 Feb 27, 2021
 #2
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x ^2     +   (x-2)^2 = 650

x ^2 + x^2 -4x+4 = 650

2 x^2 -4x - 646 = 0

 

x = 19     x-2 =17

 Feb 27, 2021

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