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Question

Find two consecutive odd natural numbers, the sum of whose squares is 202.

Solution
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Let the two odd consecutive numbers xand(x+2)

According to given question, we have

x2+(x+2)2=202

x2+x2+4+4x=202

2x2+4x=198

x2+2x=99

x2+2x99=0

x2+(119)x99=0

x2+11x9x99=0

x(x+11)9(x+11)=0

(x+11)(x9)=0

(x+11)=0or,(x9)=0

x=9 [x11,as it is a not a natural number]

And, x+2=9+2=11

Hence, two consecutive odd natural numbers are 9 and 11.

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