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प्रश्न
The sum of the squares of two consecutive positive integers is 365. Find the integers.
उत्तर
Let the required two consecutive positive integers be x and (x+1).
According to the given condition,
`x^2+(x+1)^2=365`
⇒`x^2+x^2+2x+1=365`
⇒`2x^2+2x-364=0`
⇒`x^2+x-182=0`
⇒`x^2+14x-13x-182=0`
⇒`x(x+14)-13(x+14)=0`
⇒`(x+14)(x-13)=0`
⇒`x+14=0 or x-13`
∴`x=13` (x is a positive integers)
When `x=13`
`x+1=13+1=14`
Hence, the required positive integers are 13 and 14.
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