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Q.

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


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a

 12 and 14

b

14 and 16

c

16 and 18

d

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,
⇒x2+(x+2)2=394⇒x2+x2+4x+4=394⇒2x2+4x-390=0⇒x2+2x-195=0⇒x2+15x-13x-195=0⇒x(x+15)-13(x+15)=0⇒(x-13)(x+15)=0⇒x-13=0 or x+15=0⇒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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