Question

2.दोन क्रमागत सम नैसर्गिक संख्यांच्या वर्गाची बेरीज 244 आहे, तर त्या संख्या शोधा.​

Answer 1

SOLUTION

GIVEN

The sum of the squares of two consecutive even natural numbers is 244,

TO DETERMINE

The numbers.

EVALUATION

Let the two consecutive even natural numbers are 2n and 2n + 2

So by the given condition

$\sf{ {(2n)}^{2} + {(2n + 2)}^{2} = 244}$

$\sf{ \implies \: 4 {n}^{2} + 4{(n + 1)}^{2} = 244}$

$\sf{ \implies \: {n}^{2} + {(n + 1)}^{2} = 61}$

$\sf{ \implies \: {n}^{2} + {n}^{2} + 2n + 1 = 61}$

$\sf{ \implies \: 2{n}^{2} + 2n - 60 =0}$

$\sf{ \implies \: {n}^{2} + n - 30 =0}$

$\sf{ \implies \: {n}^{2} + 6n - 5n - 30 =0}$

$\sf{ \implies \: (n + 6)(n - 5)=0}$

$\sf{ \implies \: n = - 6 \:, \: 5}$

Since n is a natural number

$\sf{n \ne - 6}$

∴ n = 5

Hence the required two consecutive even natural numbers are 10 and 12

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