I once saw a method of proving tht 2=1 It started a=b therfore ab= a "squared" Does anyone know the rest??

Answer 1

Let a = b = 1.

a = b [Given]
a ^2 = ab [Multiplying a on both sides]
a^2 - b^2 = ab - b^2 [Subtracting b^2 on both sides]
(a + b)(a - b) = b(a - b) [Factoring both sides]
(a + b) = b [Dividing both sides by (a - b)]
(1 + 1) = 1 [Substitution]
2 = 1

The flaw in this so-called "proof" is that you can't divide both sides of an equation by (a - b), because with a = b, a - b = 0, and you can't divide a number by zero.

Answer 2

a=b=1

Answer 3

A proof that 1 = 2:



1^2 – 1^2 = (1 – 1)x(1 + 1)

(1 – 1) = (1 – 1)x(1 + 1)

(1 – 1) ÷ (1 – 1) = (1 + 1)

1 = 2



DANGER: don’t show this to your math teacher…giggles

Answer 4

Let a = b
Multiply both sides by a: ab = a^2
Subtract b^2 from both sides: ab - b^2 = a^2 - b^2
Factor both sides: b(a - b) = (a+b)(a-b)
Divide both sides by (a-b): b = a+b
Since b = a, substitute b for a: b = b + b
Add: b = 2b
Divide both sides by b: 1 = 2

Of course, the flaw is that since a = b, when you divide both sides by (a-b), you're actually dividing both sides by zero, which causes black holes, the Bermuda Triangle, and Florida election miscounts.

Answer 5

This is it
a = b = 1
a^2 = ab
a^2 - b^2 = ab - b^2
(a - b)(a + b) = b(a - b)
and than dividing by (a-b)
to get (a+b)=b so 2 = 1

but actually it's wrong because a-b = 0 and you cannot divide by 0

Answer 6

Start
a = b

multiply by a
a² = ab

add -b² to both sides
a² - b² = ab - b²

factor both sides
(a + b)(a - b) = b(a - b)

Divide both sides by a - b
a + b = b

From the beginning, a = b (substitute)
b + b = b

Combine like terms
2b = b

Divide both sides by b
2 = 1

QED
^_^

Answer 7

hey here's it
a=b
ab=b^2
(ab - a)=(b^2 - 1)
a(b-1) = (b+1)(b-1)
a=(b+1)

so if b=1
a=b+1 = 2
1=2

Bt there is a fundamental mistake in it! try to find out

Answer 8

x^2 - x^2 = x^2 - x^2

x(x-x) = (x + x) (x - x) i.e Difference of two squares

Cancel out from both sides: (x - x)

Therefore: x = (x + x)

x = 2x

Therefore 1 = 2

Answer 9

You can look up those kinds of things on wikipedia, I think under logical fallacy searches, or flawed logic, false theories-- something like that.

They're flawed, though, and it explains why. There are several.

Answer 10

This may seem a little silly but here goes...

a = b = 1

a^2 = a.b

d(a^2)/da = d(a.b)/da

2a = b

2 = 1

oh my ;)