Quote:
Originally Posted by Moshi2
There's the error in bold. To simplify (A+ B )(A-B ) = B(A- B ), what did you do? dividing both sides by (A- B ), right? BUT, A-B = 0 (based on your assumption A= B ) [division by zero]
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Yup. Division by zero. here is the same equation (x=y instead) and the solution from a math site:
Here’s our “proof”
1. Let x = y
2. so
x2 = xy
3. adding x2 to both sides of the equation we get
x2 + x2 = x2 + xy
4. simplifying we get
2 x2 = x2 + xy
5. subtract 2xy from both sides and we get
2 x2– 2xy = x2 + xy – 2xy
6. simplifying we get
2 x2– 2xy = x2– xy
7. factoring for (x2– xy) we get
2 (x2– xy) = 1 (x2– xy)
8. divide both sides by (x2– xy) we get
2 = 1
The problem with our proof is in step 8:
8. divide both sides by (x2– xy) we get
2 = 1
Answer:
In step 1 we said that x = y so (x2– xy) = 0 and you can’t divide by 0.
Our flawed proof is a good example of why dividing by 0 is not allowed. It’s not just because your math teacher told you so. It is because dividing by 0 can produce impossible results.