Question

the sum of the squares of two consecutive natural numbers is 365 . find numbers

Answer 1

13^2+14^2. 169+196=365. So, the numbers are 13 and 14.

Answer 2

To solve this type of question
Let the first number is x
Because it is consecutive
The 2nd number be (x+1)
Now;
Acc. to the condition
x^2+(x+1)^2 =365
= x^2+ (x^2+1+2x) =365
=2x^2+2x+1=365
=2x^2+2x-364=0
=x^2 +x-182 =0 (taking 2common)
= x^2+14x-13x-182=0
=> x(x+14)-13(x+14)=0
=> x= -14 and 13
-ve value is neglected
Hence,
1st number is 13 and
2nd is (13+1)=14 answer