Question

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

Answer 1

Answer:

Since the numbers are consecutive, the other number would be x+1. Square both and add together to equal 313. given numbers are natural . so x=12 and x+1=13 are the two numbers.

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

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