Mathematical fallacy (inspired)

Number Theory Level 2

In the following 6 lines, it is given that a = b a=b :

a 2 − b 2 = a 2 − a b ⇒ ( a + b ) ( a − b ) = a ( a − b ) ⇒ ( a + b ) = a ⇒ a + a = a ⇒ 2 a = a ⇒ 2 = 1 { a }^{ 2 }-{ b }^{ 2 }= { a }^{ 2 }-ab\\ \\ \Rightarrow (a+b)(a-b) = a(a-b)\\ \\ \Rightarrow (a+b) = a\\ \\ \Rightarrow a+a = a\\ \\ \Rightarrow 2a = a\\ \\ \Rightarrow 2 = 1

Which line is wrong?

1 2 4 3

Shivam K by Shivam K , 21, India

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1 solution

Edward Gelernt
Mar 13, 2016

Since a=b, a-b=0, and thus you can't divide by it.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Dats d reason!!!! And it is one of the misconceptions!

Shivam K - 5 years, 3 months ago

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