Question

find two consecutive odd natural numbers the sum of whose squares is 395​

Answer 1

Answer:

Let two consecutive odd number be x and x+2

According to the question,

⇒ x

2

+(x+2)

2

=394

⇒ x

2

+x

2

+4x+4=394

⇒ 2x

2

+4x−390=0

⇒ x

2

+2x−195=0

⇒ x

2

+15x−13x−195=0

⇒ x(x+15)−13(x+15)=0

⇒ (x+15)(x−13)=0

⇒ x+15=0 and x−13=0

⇒ x=−15 and x=13

∴ On number is 13

⇒ Other number =13+2=15

⇒ Required product =13×15=195