Question

The sum of the squares of 2 consecutive odd number is 394.Find the numbers

Answer 1

Let the two consecutive odd numbers be x and x+2
X² + (X+2)² = 394
X² + X² + 4X + 22 = 394
2X² + 4X + 4 = 394     
X² +2X =(394 - 4)/2
X² + 2X = 195
X²+2X - 195 = 0
X² + 15X - 13X -195 = 0    .
X( X + 15 ) - 13( X + 15 ) = 0
( X + 15 ) ( X - 13 )

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x+15=0
x=-15
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x-13=0
x=+13
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We are taking the value of x to be 13 as it is a positive number.
And (x+2)=13+2  =15

Hence, the two consecutive numbers are 13,15.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the first odd no. be 2x + 1

Second consecutive  odd number

= 2x + 1 + 2

= 2x + 3

Now, according to the question

⇒ (2x + 1)² + (2x + 3)² = 394

⇒ 4x² + 4x + 1 + 4x² + 12x + 9 = 394

⇒ 8x² + 16x - 384 = 0

⇒ x² + 2x - 48 = 0

⇒ x² + 8x - 6x - 48 = 0

⇒ x(x + 8) - 6(x + 8) = 0

⇒ x = -8 or 6

First No = 2 × 6 + 1 = 13

Second odd no. = 15