Question

Find two consecutive odd natural number sum of whose square is 394.?

Answer 1

Answer:

The numbers are 13 and 15

Step-by-step explanation:

Let,

First consecutive odd no. = x

Second consecutive odd no. = x + 2

According to question:

⇒ (x)² + (x + 2)² = 394

⇒ x² + x² + 4x + 4 = 394

⇒ 2x² + 4x + 4 = 394

⇒ 2x² + 4x = 394 - 4

⇒ 2x² + 4x = 390

⇒ 2x² + 4x - 390 = 0 -------- (Divide it by 2)

⇒ x² + 2x - 195 = 0

⇒ x² + 15x - 13x - 195 = 0

⇒ x (x + 15) - 13 (x + 15) = 0

⇒ (x - 13) (x + 15) = 0

⇒ x = 13 , x = - 15

Hence,

⇒ x = 13

Therefore,

The numbers are 13 and 15

Answer 2

Given ,

The sum of square of two consecutive odd natural number is 394

Let , the two consecutive odd natural numbers be " x " and " x + 2 "

Thus ,

(x)² + (x + 2)² = 394

(x)² + (x)² + 4 + 4x = 394

2(x)² + 4x - 390 = 0

(x)² + 2x - 195 = 0

By middle term splitting method , we get

(x)² + 15x - 13x - 195 = 0

x(x + 15) - 13(x + 15) = 0

(x - 13)(x + 15) = 0

x = 13 or x = -15

Since , the two consecutive odd numbers are natural numbers

$\sf \therefore \underline{The \: two \: consecutive \: odd \: natural \: numbers \: are \: 13 \: and \: 15}$