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Question
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Solution
Let the two consecutive positive odd numbers be x and (x+2).
According to the given condition
`x^2+(x+2)^2=514`
⇒`x^2+x^2+4x+4=514`
⇒`2x^2+4x-510=0`
⇒`x^2+2x-255=0`
⇒`x^2+17x-15x-255=0`
⇒`x(x+17)-15(x+17)=0`
⇒`(x+17)(x-15)=0`
⇒`x+17=0` or `x-15=0`
⇒`x=-17 or x-15`
∴`x=15` (x is a positive odd number)
When `x=15`
`x+2=15+2=17`
Hence, the required positive integers are 15 and 17.
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