1.

Sum of the squares of two consecutive natural numbers is 313 find the natural number​

Answer»

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ASSUMPTION,

FIRST consecutive NUMBER be p

ALSO,

Second consecutive number be p + 1

Now,

Situation,

⇒ p² + (p + 1)² = 313

⇒ 2p² + 2p + 1 = 313

⇒ 2p² + 2p - 312 = 0 ...... (1)

Now,

Divide (1) by 2

⇒ p² + p - 156 = 0

⇒ p² + 13p - 12p - 156 = 0

⇒ p(p + 13) - 12(p + 13) = 0

⇒ (p + 13) (p - 12) = 0

⇒ p + 13 = 0

⇒ p = -13 (Not possible)

Also,

⇒ p - 12 = 0

⇒ p = 12

⇒ p = 12

Hence,

First number = p = 12

Second number = p + 1 = 12 + 1 = 13


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