Date registered: Aug 2002
Vehicle: 190E, 400E, SLK350
Location: Chesapeak Bay
Mentioned: 1 Post(s)
Quoted: 983 Post(s)
Ok, let me help you
so we start with this equality: x^n + y^n = Z^n but we want to prove that it's not an equality, that is there are no solutions to prove said equality.
Ok, let's do this:
Suppose I do this: ((z^n)^2)^1/2 do you agree that it will give me back z^n?
if so, then let's do that to the other side of the equality:
((x^n + y^n)^2)^1/2 are you ok with that?
if so, then let's expand that a little bit:
((x^n + y^n)(x^n + y^n))^1/2 so far so good?
Let's multiply the members:
(x^2n + 2x^n.y^n + y^2n)^1/2 = z^n You're still with me?
What about I square both sides?
x^2n + 2x^n.y^n + y^2n = z^2n
Now the interesting part: suppose m = 2n
we get back:
x^m + y^m + 2x^m/2. y^m/2 = z^m
Wait a minute! do you see something? Did you just see what happened?
if x^m + y^m can be equal to z^m then we prove equality if we can prove that we can have x and y where 2x^m/2. y^m/2 = 0. Is this possible for x and y never being zero?
Do you see anything wrong with my approach? I have a feeling I made a booboo somewhere but then again, it's Sunday morning.