let x2, now write proof for (x^3)8,

i was supposed to derive the answer from answering a former question, let x2, now write proof for (x^2)4.
The answer was,
since x2, x is real and x 0.
by multiply by x, (x^2)2x,
since 20, by multiplying 2, 2x4.
Through transitivity -, (x^2)4.

but i cant derive answer. help tks

Question

let x>2, now write proof for (x^3)>8,

i was supposed to derive the answer from answering a former question, let x>2, now write proof for (x^2)>4.
The answer was, 
since x>2, x is real and x >0.
by multiply by x, (x^2)>2x,
since 2>0, by multiplying 2, 2x>4.
Through transitivity ->, (x^2)>4.

but i cant derive answer. help tks

zzr0ck3r · Answer

2<x
so of course x>0
2^3<x^3 --> 8<x^3

anonymous · Answer

i need to write proper proof.

zzr0ck3r · Answer

this is a proper proof
assume x>2
then by transitivity x>0
since x>0 x>2 iff x^2>4 iff x^3>8
qed.

anonymous · Answer

since x>0, x>2 iff x^2>4 iff x^3>8? then how do i proof x^2>4 and x^3>8? if just proven, isn't it only vacuously true?

caozeyuan · Answer

you have proven that x^2>4  that is x^3>4x, you agree? then, since x>2, 4x>8, thus, x^3>8. You see, nice and easy!

anonymous · Answer

omg, how can i not think of this? thank you!

caozeyuan · Answer

could you please take a look at the question I just posted? thx!