Question

Find the error in the derivation:

Given, a=b__eq^n 1
*Multiplying by 'a' on both side*
Therefore, a^2=ab
*Subtracting 'b^2' from both sides*
Therefore, a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
*Cancelling "(a-b)" from both sides*
Therefore, (a+b)=b
*Substitute eq^n 1*
(a+a)=a
2a=a
*Cancelling 'a' from both sides*
Hence, 2=1.

Answer 1

It is a good question!

Undefined Values :

    The value 0/0, 1/0, ... are called undefined or intermediate values; it means that we cannot apply these forms in answers, and applying them will be incorrect in normal calculations.

I start from the following step :

(a + b) (a - b) = b (a - b) .....(i)

Given that, a = b ⇒ a - b = 0

From (i), we get

(a + b) * 0 = b * 0 .....(ii)

    We can get a + b = b only when we will multiply both sides of (ii) by 1/0, i.e., reciprocal of 0 and we know that 1/0 is an undefined value.

Taking 1/0 as a finite value is the error.

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