1+1 = 1?

Algebra Level 3

Look at this proof

let x = 1 , $x^2$ =1 , $x^2=x$ -----------------------------(1)

then $x^2-1=x-1$ , $(x-1)(x+1)=x-1$ -----------------(2)

so , $x+1 = 1$ , which is equal to 2=1 Q.E.D---------(3)

Where did the "proof" get wrong ?

1 math is magical 2 3

2 solutions

Abdur Rehman Zahid
Dec 3, 2014

If $x=1$ then $x-1=0$ .In (3) you are assuming the result of dividing both sides by $x-1\rightarrow 0$ as one which not allowed so answer is $\boxed{(3)}$

Math Man
Sep 1, 2014

x-1=0 , so it is forbidden to divide by 0

But the mistake has been done in the second line...then why i go to the second line to find the wrong?

Hemel Sarkar - 6 years, 9 months ago

the "dividing" is at the 3rd line

math man - 6 years, 9 months ago

0=0 is a mistake in itself

Shriram Raghav - 6 years, 9 months ago

@Shriram Raghav – Nah! I think 0=0 is perfectly normal, thank you very much. #HP

Satvik Golechha - 6 years, 7 months ago

1+1 = 1?

2 solutions

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