Question

find two consecutive positive integers sum of whose squares is 365
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Answer 1

Answer:

13 and 14

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.

hope it helps!!!!

Answer 2

Answer:

Let the consecutive numbers be x,x+1

Sum of their squares x  

2  +(x+1)  2

=365 x  

2  +x  

2  +2x+1=365 2x  2

+2x−364=0 x  2

+x−182=0x  2

+14x−13x−182=0

x(x+14)−13(x+14)=0

(x+14)(x−13)=0

x=−14,13

x=13  

two consecutive positive integers=13,14