Question

find two consecutive odd natural numbers the sum of whose squares is 395​

Answer 1

Step-by-step explanation:

let, x and (x + 2) are those consecutive odd natural numbers. according to question

given, sum of squares = 130

x^2 + (x + 2)^2 = 130

x^2 + x^2 + 4x +4=130

2x^2 + 4x=126

2(x^2 + 2x) = 126

x^2 + 2x = 63

x^2 + 2x - 63 = 0

x^2 + 9x - 7x - 63 = 0

x(x + 9) -7 (x +9)=0

(x-7)(x + 9) = 0

x - 7=0, x + 9 =0

x = 7, x = -9

natural numbers can not be considered as negative. so take positive value of 'x'

now the required numbers are

x = 7, x + 2 = 7+2=9

therefore, the required consecutive odd natural numbers sum of whose squares is 130 are 7 and 9.

Your Answer: 7,9

Answer 2

QUESTION:

• Find two consecutive odd natural numbers the sum of whose squares is 394

ANSWER:

Given:

• Sum of 2 consecutive odd natural numbers = 394

To Find:

• The 2 numbers.

Solution:

Let us assume that the 2 consecutive odd natural numbers are (2x - 1) and (2x + 1) respectively.

Acc to question,

⇒ (2x - 1)² + (2x + 1)² = 394

We know that,

⇒ (a ± b)² = a² + b² ± 2ab

So,

⇒ (2x - 1)² + (2x + 1)² = 394

⇒ 4x² + 1 - 4x + 4x² + 1 + 4x = 394

⇒ 8x² + 2 = 394

⇒ 8x² = 394 - 2

⇒ 8x² = 392

⇒ x² = 392/8

⇒ x² = 49

⇒ x = ±7

As, we need to find natural numbers, we will take x = 7.

So, the numbers are:

• 2x - 1 = 2(7) - 1 = 14 - 1 = 13
• 2x + 1 = 2(7) + 1 = 14 + 1 = 15

Therefore, the 2 consecutive odd natural numbers whose sum of whose squares is 394 are 13 and 15 respectively.

Formula Used:

• (a ± b)² = a² + b² ± 2ab