Taking out factors !!!
Algebra
Level
3
Find the number of unordered pairs ( x , y ) which satisfies the given equation :
- = 2007196
The answer is 0.
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
The answer to the above question is 0
Basically It has nothing to do with the no of factors of the given number 2007196.
The LHS can be written as
( x - y ) ( x + y ) ( x 2 + y 2 ) = 2007196
For the expression to satisfy LHS must be even ie, either ( x- y ) or ( x+ y) or ( x^2 + y^2 ) must be even
=> either both x,y must be even ; or both x,y must be odd.
In either case x,y { even / odd } all the factors of the LHS is even
Hence ( x - y ) ( x+ y ) ( x 2 + y 2 ) is a multiple of 8 whereas
the RHS 2007196 is a multiple of 4 ;
So there is no value of x and y which satisfies the given expression :
Hence the NUMBER OF PAIRS ( X , Y ) is 0