SOLUTION: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw?
Let a and b be any two different numbers. Define x as the differenc
Question 150442: The following appears to prove that any two numbers are equal. Obviously it is wrong; can you spot the flaw?
Let a and b be any two different numbers. Define x as the difference between them:
x = b - a
Multiply both sides of the equation by (b-a):
x(b – a) = (b – a)(b – a)
bx – ax = b^2 – 2ab + a^2
Add –bx+ab-a^2 to both sides and simplify:
bx – ax – bx + ab – a^2 = b^2 – 2ab + a^2 – bx + ab – a^2
bx – bx – ax + ab – a^2 = –bx + b^2 – 2ab + ab + a^2 – a^2
–ax + ab – a^2 = –bx + b^2 – ab
Both sides of this equation have a common factor:
a(–x + b – a) = b(–x + b – a)
Divide both sides by (-x+b-a):
a(–x + b – a)/-x + b-a = b(–x + b – a)/ -x + b - a
a = b
You can put this solution on YOUR website! You said "Divide both sides by (-x+b-a)"
But what is x?
x = b-a
So what is (-x + b -a)?
(-b + a + b - a) = 0
You can make 'anything' happen if you allow division by zero. Which is why division by zero is undefined.
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