Question

Find two consecutive positive integers, sum of whose squares is 365.​

Answer 1

Step-by-step explanation:

Let the two consecutive positive integers be x and x+1

Then,

x

2

+(x+1)

2

=365

⇒x

2

+x

2

+2x+1=365

⇒2x

2

+2x−364=0

⇒x

2

+x−182=0

Using the quadratic formula, we get

x=

2

−1±

1+728

⇒

2

−1±27

⇒x=13 and x=−14

But x is given to be a positive integer. ∴x



=−14

Hence, the two consecutive positive integers are 13 and 14.

Answer 2

Answer:

Correct option is A)

Let the two consecutive positive integers be x and x+1

Then,

x

2

+(x+1)

2

=365

⇒x

2

+x

2

+2x+1=365

⇒2x

2

+2x−364=0

⇒x

2

+x−182=0

Using the quadratic formula, we get

x=

2

−1±

1+728

⇒

2

−1±27

⇒x=13 and x=−14

But x is given to be a positive integer. ∴x



=−14

Hence, the two consecutive positive integers are 13 and 14.