2=1 is false, prove that it's false!

Algebra Level 1

Let a=1 and b=1 Hence, a=b Multiplying both sides with a, we get:- a^2 = ab subtracting b^2 from both sides, we get:- a^2 - b^2 = ab-b^2 and.... (a + b)(a - b) = b(a -b) So, (a -b) gets cancelled on both sides, and we are left with a + b = b Re-substituting, we get, 1 + 1 = 1 2=1 We all know that it's not true! So post the mistake in this solving..........or you must believe that it's true! THIS PROBLEM IS JUST FREE POINTS FOR YOU!!!! CHOOSE THE ANSWER AS :- I KNOW IT!!! and get it correct ; but please explain how this is wrong!

I KNOW IT!!! I am not the correct answer! Don't click on me! Click on me!

Shubham Thakkar by Shubham Thakkar , 24, India

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10 solutions

Mihir Mistry
May 27, 2014

U cannot cancel a-b since its value is 0

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Right answer!

Shubham Thakkar - 6 years, 10 months ago

You cann't divide (a+b)(a-b)=b(a-b) by (a-b) on both sides because (a-b) is zero. Similar case with do anybody have reasons for this??

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ipshit Shaha
Dec 17, 2015

The step where a-b is cancelled from both sides is wrong.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ashish Menon
Dec 17, 2015

a - b = 0-0 = 0. Now when we cancel a - b on both sides, weare dividing byzero,which can be any number.a

0 Helpful 0 Interesting 0 Brilliant 0 Confused

since, a=b... therefore a-b=0...... so we cannot cancel it

0 Helpful 0 Interesting 0 Brilliant 0 Confused

We can't divide by a-b, because it's 0

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Aishwarya Gavai
Jul 23, 2014

u can't cancel (a-b) since a=b, OR a-b=0

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Ahmed Abdelbasit
Jun 4, 2014

the cancelled term(a-b) is equal to 0 .. so it is wrong to cancel it .. because the zero term is the only condition of equality in equations , so; it can not be cancelled yet ...

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Dhanashree J
May 27, 2014

a-b=0

so you cannot cancel it.

:D While solving a problem in limits,I also ended up with a bizarre solution 5=8! With a few wrong assumptions this can happen.

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Adeeb Zaman
May 27, 2014

2x0=1x0 Dividing by 0, we don't quite get 2=1 :P

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