Question

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

Answer 1

Hi Mate!!!

Conservative No.s :- No.s which are one after another.

E.g :- 5 and 5 +1 are consecutive no.s

Exp:-

Let the no. be x

it's consecutive is x +1

According to the question.

x² + ( x + 1 )² = 313

x² + x -156=0

x = - 1 + √{ ( 1 ) ² + 224 } / 2 or x = {-1 - √ ( 1 )
224 } / 2

x = 7 or x = -8

Answer 2

⠀⠀⠀⠀☯ Let two consecutive natural numbers be x and x + 1.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: According\: to \: the \: Question :}}}}}\mid}$

$\qquad:\implies\sf x^2 + (x + 1)^2 = 313\qquad\qquad\bigg\lgroup\bf Given \bigg\rgroup$

$:\implies\sf x^2 + x^2 + 2x + 1 = 313$

$:\implies\sf 2x^2 + 2x + 1 = 313$

$:\implies\sf 2x^2 + 2x + 1 - 313 = 0$

$:\implies\sf 2x^2 + 2x - 312 = 0$

$:\implies\sf 2(x^2 + x - 156) = 0$

$:\implies\sf x^2 + x - 156 = 0$

$:\implies\sf x^2 + 13x - 12x - 156 = 0$

$:\implies\sf x(x + 13) - 12(x + 13) = 0$

$:\implies\sf (x + 13)(x - 12) = 0$

$:\implies\sf x + 13 = 0\;or\; x - 12 = 0$

$:\implies\bf x = 12\;or\;x = -13$

☯ Since x, being a natural number, can't be negative.

Therefore,

• x = 12

• x + 1 = 13

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