Question

the sum of square of two consecutive natural number is 313 find the number

Answer 1

let one number be x
other number = (x+1)

ATQ,
x²+(x+1)² = 313
x²+x²+2x+1 = 313
2x²+2x-312 = 0
x²+x-156 = 0

so,
x = 12 or -13

so, the numbers are 12,13 or -13,-12

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the 1st consecutive natural number be x.

And the 2nd consecutive natural number be x + 1.

Then,

According to the Question,

⇒ x² + (x + 1)² = 313

⇒ 2x² + 2x + 1 = 313

⇒ 2x² + 2x - 312 = 0

Dividing Eq by 2, we get

⇒ x² + x - 156 = 0

By using factorization method, we get

⇒ x² + x - 156 = 0

⇒ x² + 13x - 12x - 156 = 0

⇒ x(x + 13) - 12(x + 13) = 0

⇒ (x + 13) (x - 12) = 0

⇒ x + 13 = 0 or x - 12 = 0

⇒ x = - 13, 12  (As x can't be negative)

⇒ x = 12

1st number = x = 12

2nd number = x + 1 = 12 + 1 = 13

Hence, the two natural consecutive numbers are 12  and 13.