Xcell X.
asked • 10/23/17proof that x+y=2xy
Proof for the equation that x+y=2xy using whatever method.
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2 Answers By Expert Tutors
Inactive Tutor answered • 10/23/17
Tutor
New to Wyzant
Can you think of it further? You can't just say it can't be proven. X and Y are complete variables.
Inactive Tutor
Can you prove that (a+b)^2=a^2+b^2+2ab.
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10/23/17
Inactive Tutor
Certainly!
(a + b)(a + b)= a2 + ab + ba + b2 = a2 + 2ab + b2
This is true for any real or complex a and b. But
x + y = 2xy
is not true in general, for any real or complex x and y. As I have said, you can solve for a family of x and y values that satisfy the equation, but to prove the equation, it would have to be true for all x and y, which it obviously is not.
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10/23/17
Inactive Tutor
Can you also reason well that 1+1=0 ?
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10/23/17
Inactive Tutor answered • 10/23/17
Tutor
New to Wyzant
This cannot be proven because it is not true in general.
Example:
x = 2
y = 3
x + y = 2 + 3 = 5 ≠ 2(2)(3)
However, you can express one variable in terms of the other, but that is not the same as a proof.
x + y = 2xy
2xy - y = x
y(2x - 1) = x
y = x/(2x - 1) [with restriction that x ≠ 1/2]
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Inactive Tutor
10/23/17