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

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12 and 14

14 and 16

16 and 18

13 and 15

answer is A.

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Detailed Solution

Suppose
The one number be x then the other number be x+2.
Then according to question,

\Rightarrow x^{2} + (x + 2)^{2} = 394 \Rightarrow x^{2} + x^{2} + 4 x + 4 = 394 \Rightarrow 2 x^{2} + 4 x - 390 = 0 \Rightarrow x^{2} + 2 x - 195 = 0 \Rightarrow x^{2} + 15 x - 13 x - 195 = 0 \Rightarrow x (x + 15) - 13 (x + 15) = 0 \Rightarrow (x - 13) (x + 15) = 0 \Rightarrow x - 13 = 0 or x + 15 = 0 \Rightarrow x = 13 or x = - 15

Here, x being an odd number,
Therefore, x=13.
Thus, the two consecutive odd number are 13 and 15.
Correct option is 4.

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