Question

the sum of squares of 3 consecutive odd natural numbers is 515 . find the nos

Answer 1

Answer:

11,13,15

Step-by-step explanation:

As numbers are consecutive 'odd', they must lie after a gap of '2', so, let the numbers are 'a - 2, 'a' and 'a + 2'.

According to question:

=> sum of squares = 515

=> (a - 2)² + a² + (a + 2)² = 515

=> (a² + 4 + 4a) + a² + (a² + 4 + 4a) = 515

=> 3a² + 8 = 515

=> 3a² = 515 - 8 = 507

=> a² = 507/3 = 169

=> a = √169 = 13

Therefore, numbers are:

a - 2 = 13 - 2 = 11

a = 13

a + 2 = 13 + 2 = 15

Answer 2

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• The unknown numbers

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Let the numbers are a - 2, a and a + 2

A.T.Q :-

⇢ Sum of squares = 515

⇢ (a - 2)² + a² + (a + 2)² = 515

⇢ (a² + 4 + 4a) + a² + (a² + 4 + 4a) = 515

⇢ 3a² + 8 = 515

⇢ 3a² = 515 - 8

⇢ a = √169

⇢ a = 13

Hence

__________

The numbers are :-

• a - 2 = 11

• a - 2 = 13

• a - 2 = 15

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