Question

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

Answer 1

Answer:

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

Then,

x2+(x+1)2=365

⇒x2+x2+2x+1=365

⇒2x2+2x−364=0

⇒x2+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

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

Then,

x2+(x+1)2=365

⇒x2+x2+2x+1=365

⇒2x2+2x−364=0

⇒x2+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.