Find two consecutive odd natural numbers, the sum of whose square is 394.
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Consider one number be (2n−1), then the next consecutive odd number will be (2n+1)
⇒(2n−1)
2
+(2n+1)
2
=394
⇒4n
2
+1−4n+4n
2
+1+4n=394
⇒8n
2
+2=394
⇒8n
2
=392
⇒n
2
=49
⇒n=7
Therefore, the two consecutive numbers are
(2n−1)=14−1=13
(2n+1)=14+1=15
Hence, the two consecutive numbers are 13 and 15
Step-by-step explanation:
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