Correct-Incorrect Equation

let a=b

a^2=ab

a^2-b^2=ab-b^2

(a+b)(a-b)=b(a-b)

a+b=b

2b=b

2=1

This series of equations is given to prove that 2=1.Although this may appear correct there is a fallacy in this.At step 5 both sides have been divided by a-b.But a=b.So a-b=o.An d, no number can be divided by 0.

#Algebra

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

We had that too in a quiz after we discussed trigonometric ratios :D The questions was "Prove that 2=1" I kept going to 1=0 until we were given a hint - difference of two squares :D

Marc Vince Casimiro - 6 years, 5 months ago

i found a solution when we compare 1=2 with a=b => a is not equal to b thats it any doubts reply me ill say

sudoku subbu - 6 years, 4 months ago

I had given the solution that it is incorrect.Then how can you give a solution for a incorrect question

Vishal S - 6 years, 4 months ago

that's what iam saying a is not = b you considered a wrong equation in the beggening

sudoku subbu - 6 years, 4 months ago

@Sudoku Subbu – How can you tell that $a \neq b$ .I had provided the word let a=b.If a=b in the above series of equation, we get 1=2

Vishal S - 6 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$