2 positive no.s such that................

Algebra Level 2

There are 2 consecutive positive integers such that the sum of whose squares is 365. Find the smaller of the 2 numbers. Note: Negative numbers are inadmissible.


The answer is 13.

Satyajit Ghosh by Satyajit Ghosh , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Ronak Agarwal
Aug 22, 2014

Let the numbers be x , x + 1 x,x+1 .

Then we have x 2 + ( x + 1 ) 2 = 365 {x}^{2}+{(x+1)}^{2}=365

Simplifying we have :

x 2 + x − 182 = 0 {x}^{2}+x-182=0

Hence we have ( x + 14 ) ( x − 13 ) = 0 (x+14)(x-13)=0

⇒ x = 13 , − 14 \Rightarrow x= 13,-14 but since negative numbers are inadmissible hence x = 13 x=13

Finally we get the smaller number as 13 13

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...