Question

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

Answer 1

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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Answer 2

Answer:

x²+( x+1)²=365

⇒x²+x²+1+2x=365

⇒2x²+2x=364

⇒2x²+2x-364=0

⇒x²+x-182=0

⇒x²-14x+13x-182=0

⇒x(x-14)+13(x-14)=0

⇒(x-14)(x+13)=0

⇒x=14                                          [∵x≠ -13 not a positive integer]

now,1st no. isx= 14 and x+1=14+1=15

hence,the required two consecutive positive integer are 14 and 15.

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Step-by-step explanation: