Proofing weird things 1

Number Theory Level 2

Step 1: x = y 

        x^2 = xy

        x^2 - y^2 = xy - y^2

        (x - y)(x + y) = y(x - y)

Step 2:(x - y)(x + y)/(x - y) = y(x - y)/(x - y)

Step 3:x + y = y

Step 4:y + y = y

2y = y

2 = 1

Hence we proved 2 = 1

Which is the wrong step in the given solution?

Step 1 All the steps are correct and the proof is true. Step 3 Step 2

Tanveen Dhingra by tanveen dhingra , 19, 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.

2 solutions

Ritu Roy
Nov 9, 2014

G i v e n , x = y w h i c h m e a n s , x + y = 2 x = 2 y & x − y = 0 ( x − y ) ( x + y ) / ( x − y ) = y ( x − y ) / ( x − y ) w h i c h m e a n s ( 0 ) ( x + y ) / ( 0 ) = y ( 0 ) / ( 0 ) D i v i s i o n b y z e r o i s u n d e f i n e d . T h u s S t e p 2 i s i n c o r r e c t . T h i s s a m e q u e s t i o n i s s e e n i n o t h e r B r i l l i a n t q u e s t i o n s t o o . Given,\quad x=y\\ which\quad means,\\ x+y=2x=2y\\ \& \quad x-y=0\\ \\ \\ (x-y)(x+y)/(x-y)=y(x-y)/(x-y)\\ which\quad means\\ (0)(x+y)/(0)=y(0)/(0)\\ Division\quad by\quad zero\quad is\quad undefined.\\ Thus\quad Step\quad 2\quad is\quad incorrect.\\ This\quad same\quad question\quad is\quad seen\quad in\quad other\\ Brilliant\quad questions\quad too.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Saurav Suman
Nov 9, 2014

You cannot divide any no by zero, here in the step 2 you are doing the same, because x=y given.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...