1.

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

Answer»

Answer:

Correct option is

A

13,14

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.

Step-by-step explanation:

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