Question

THE SUM OF THE SQUARES OF TWO CONSECUTIVE NATURAL NO. IS 313. FIND THE NUMBERS.

Answer 1

ARYAN. PVT.......LTD.....

Answer 2

$\Large{\underline{\underline{\bf{Holamate}}}}$

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$\Large{\underline{\underline{\bf{Given:-}}}}$

The sum of the squares of two consecutive natural number is 313.

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$\Large{\underline{\underline{\bf{To\: Find:-}}}}$

Numbers = ?

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$\Large{\underline{\underline{\bf{Solution:-}}}}$

→Let one number be (x)

→And other number be (x+1)

${\bold{\underline{\underline{According\: to \: the \: Question:-}}}}$

${(x)}^{2} + {(x + 1)}^{2} = 31$

➠By using identity (a+b)² = a²+b²+2ab

$⟹{(x)}^{2} + {{x}^{2} + {1}^{2} + 2(x)(1)} = 313 \\ \\ ⟹ {x}^{2} + {x}^{2} + 1 + 2x = 313 \\ \\⟹ 2 {x}^{2} + 1 + 2x = 313 \\ \\⟹ 2 {x}^{2} + 2x = 313 - 1 \\ \\ ⟹2 {x}^{2} + 2x = 312 \\ \\ ⟹2 {x}^{2} + 2x - 312 = 0$

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${\bold{\underline{\underline{By\: middle \: term \: splitting:-}}}}$

$⟹2 {x}^{2} + 2x - 312 = 0 \\ \\ ⟹2( {x}^{2} + x - 156) = 0 \\ \\⟹ {x}^{2} + x - 156 = \frac{0}{2} \\ \\⟹ {x}^{2} + x - 156 = 0 \\ \\ ⟹{x}^{2} + 13x - 12x - 156 = 0 \\ \\ x(x + 13) - 12(x + 13) = 0 \\ \\⟹ (x - 12)(x + 13) = 0$

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${\bold{\underline{\underline{For \: zeroes\: case-1:-}}}}$

$⟹x - 12 = 0 \\ \\ ⟹x = 12$

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${\bold{\underline{\underline{For \: zeroes\: case-2:-}}}}$

$⟹x + 13 = 0 \\ \\⟹ x = - 13$

➠We cannot take negative number as it's not natural number.

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${\bold{\underline{\underline{So, the \: numbers \: are:-}}}}$

➣One number be x = 12

➣And other number be (x+1) = (12+1) = 13

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$\Large{\underline{\underline{\bf{Thanks}}}}$