2=1 proof
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Given x = 1 and y = 1, then x = y Multiplying each side by x, x2 = xy Subtracting y2 from each side, x2 - y2 = xy - y2 Factoring each side, (x + y)(x - y) = y(x - y) Dividing out the common term, (x - y) results in x + y = y Substituting the values of x and y, 1 + 1 = 1 or 2 = 1
Such a proof does not exist. With all respect to shruti, you supposed that x = 1 and y =1. Later on, you divided both sides by (x-y). But, if x = 1 and y = 1, then (x-y) = 0. In mathematical proofs, dividing both sides by 0 is not allowed.
This is not true. If you are multiplying both sides by x, then you have to exclude the fact that x could be zero. You should never divide or multiply both sides of an equation by a variable.
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