can't happen
2(a² - ab) = a² - ab and a=b
2(a² - a(a)) = a² - a(a)
2(a² - a²) = a² - a²
2(0) = 0
0 = 0
This is always true, so you could substitute anything you like for zero. However, dividing by zero is illegal; it is an undefined operation that produces weird answers like that.
My math teacher showed me that, along with:
_
.9 = 1
_
.9 = x
_
.9(10) = 10x
..._
9.9 = 10x
......._
9 + .9 = 10x
............. ..........................._
9 + x = 10x (remember x = .9)
9 = 9x
1 = x.
voila!
(sorry about the spacing and dots, but y! answers made it hard to keep the line above the .9)
2006-08-16 05:17:29
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answer #1
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answered by Anonymous
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You say there is no division involved? You are wrong. Check this out... in the 4th line of the a-b part, you have
2(a² - ab) = a² - ab
then, in line 5, you simplify to show that
2 = 1
But how did you get there? By dividing both sides by the quantity
a² - ab
which is how you simplify that equation. However, since, in line 2 you wrote that
a² = ab
then that must mean that
a² - ab = 0
and you are dividing by 0, which is not allowed.
Sorry, dude, but there is division, just not in the x = 2 + 1 + whatever part.
2006-08-16 05:22:07
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answer #2
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answered by a_strzynski 1
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Look lad, Finndo is correct. Let's see where you go wrong, okay?
a = b OK
a² = ab OK
a² + a² - 2ab = ab + a² - 2ab OK
2(a² - ab) = a² - ab OK
2 = 1 NOT OK
See, when you divide by a² - ab, you are dividing by ZERO. Why? Coz a=b, so ab=a², thus you have a²-a² which is ZERO. You cannot
divide by ZERO.
You get the idea now?
2006-08-16 07:11:13
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answer #3
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answered by Anonymous
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2 = 1 + 1
Check
x = 2 + 2 (which is 4)
Check
x = 2 + (1 +1) (still 4)
Check
1 = 2
You use this like its fact... huh?
x = 2 + (1+2) (5)
Check
X =5 for the above equation (x = 2 + (1+2)) sure, but you never proved where x = 2 + 2 is 5
2006-08-16 05:21:56
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answer #4
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answered by ? 5
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a²-ab=0
you can't divide by 0.
simplification by a²-ab IS a division by 0
you have 2*(a²-ab)=a²-ab that is to say 2*0=0, and it is perfectly correct.
But when you go to the next line, you divided by 0 and got the absurd result 2=1
2*0/0=1*0/0. Simplification by 0 = division by 0
PS: if people don't answer to your questions it's because they're an insult to maths and science. If you want mathematical truth, it's in this answer. If you prefer your lie, please feel free to believe whatever you want, but please stop presenting those false proofs on yahoo answer
2006-08-16 05:17:05
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answer #5
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answered by Anonymous
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He's right...R U ppl fine?
All the lines r fine
2(a² - ab) = a² - ab
2(a² - ab) = 1(a² - ab)
So....
2 = 1
2006-08-16 06:28:59
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answer #6
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answered by Anonymous
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Even when you are fifty, never on Earth is 2 plus 2 going to equal 5. Get over yourself, go outside and play or something.
2006-08-16 05:17:31
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answer #7
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answered by Anonymous
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ok so u say a=b well then u take a²-ab and that = 0 so when u divide by a² - ab then your dividing by zero....so your wrong you are dividing and it doesn't work...too bad you thought you thought you were so smart...mr im not an accountant im 15...lol wow
2006-08-16 05:41:12
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answer #8
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answered by Margaret W 1
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For all nonzero real numbers a and b:
a = b (Hypothesis)
(a)a = (a)b (Cancellation Law for Multiplication)
(a)a = a² (Definition of a²)
a² = ab (Substitution)
a² + a² = ab + a² (Cancellation Law for Addition)
a² = (1)a² (Indentity Axiom for Multiplication)
(1)a² + (1)a² = ab + a² (Substitution)
(1)a² + (1)a² = (1 +1)a² (Distributive Axiom)
1 + 1 = 2 (Addition Fact)
(1 +1)a² = 2a² (Substitution)
(1)a² + (1)a² = 2a² (Transitive Axiom of Equality)
2a² = ab + a² (Substitution)
ab + a² = a² + ab (Commutative Axiom for Addition)
2a² = a² + ab (Transitive Axiom of Equality)
2a² + (-ab) = a² + ab + (-ab) (Cancellation Law for Addition)
a² + ab + (-ab) = a² + [ab + (-ab)] (Associative Axiom for Addition)
ab + (-ab) = 0 (Inverse Axiom for Addition)
a² + [ab + (-ab)] = a² + 0 (Substitution)
a² + 0 = a² (Indentity for Addition)
2a² + (-ab) = a² (Transitive Axiom of Equality)
2a² + (-ab) + (-ab) = a² + (-ab) (Cancellation Law for Addition)
-ab = (-1)ab (Product of Negatives Law)
(-ab) + (-ab) = (-1)ab +(-1)ab (Substitution)
(-1)ab +(-1)ab = (-1)(ab + ab) (Distributive Axiom)
(-ab) + (-ab) = (-1)(ab + ab) (Transitive Axiom of Equality)
(1)ab = ab (Indentity for Multiplication)
ab + ab = (1)ab + (1)ab (Substitution)
(1)ab + (1)ab = (1 + 1)ab (Distributive Axiom)
(1 + 1)ab = 2ab (Substitution)
ab + ab = 2ab (Transitive Axiom of Equality)
(-1)(ab + ab) = (-1)(2ab) (Substitution)
(-ab) + (-ab) = (-1)(2ab) (Transitive Axiom of Equality)
2a² + (-1)(2ab) = a² + (-ab) (Substitution)
(-1)(2ab) = 2(-1)(ab) (Associative Axiom for Multiplication)
2a² + 2(-1)(ab) = a² + (-ab) (Substitution)
2a² + 2(-1)(ab) = 2[a² + (-1)ab] (Distributive Axiom)
(-1)ab = -ab (Symmetric Axiom of Equality)
2[a² + (-1)ab] = 2[a² + (-ab)] (Substitution)
a² + (-ab) = a² - ab (Definition of Subtraction)
2(a² - ab) = a² - ab (Substitution)
a² - ab = 1(a² - ab) (Indentity Axiom for Multiplication)
2(a² - ab) = 1(a² - ab ) (Transitive Axiom of Equality)
2(a² - ab)[1/(a² - ab)] = 1(a² - ab )[1/(a² - ab)] (Cancellation Law for Multiplication)
(a² - ab)[1/(a² - ab)] = 1 (Inverse Axiom for Multiplication)
2(1) = 2 and 1(1) = 1 (Indentity Axiom for Multiplication)
2 = 1 (Substitution)
Contradiction:
The Hypotesis states that a = b so substituting b for a:
a² - ab = (b)² - (b)b = b² - b² = 0
Hence,
(a² - ab)[1/(a² - ab)] = 0/0 and by the Inverse Axiom for Multiplication, division by zero is not allowed.
Therefore:
2 â 1
2006-08-16 11:25:31
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answer #9
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answered by Jerry M 3
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$4 in a bank at 4% interest in 5.7 years is $5, other than than Finn is right.
2006-08-16 07:48:01
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answer #10
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answered by elve_r 2
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