Question

Let a,b,c be positive real no.s such that a^3+b^3=c^3.Prove that ..

Answer 1

wait a moment

Answer 2

i dont think you can prove it beyond R^2

Answer 3

they are real numbers not integers

Answer 4

volume behaves differently than area

Answer 5

\[a ^{2}+b ^{2}-c^{2}>6(c-a)(c-b)\]

Answer 6

Have you read about Fermat's Last Theorem? ;P

Answer 7

doesn't apply here

Answer 8

im waiting for the movie :)

Answer 9

I know (we're talking about real numbers), but it reminded me of it. ;P

Me too!

Answer 10

if you want to know about Fermat's Last Theorem read Fermat's Enigma.

Answer 11

u saw that google doodle about fermat's theorem

Answer 12

When is the movie coming out amistre ?
I hope they didn't make it a vampire movie (too many of them recentlu)

Answer 13

If
\[a^3+b^3=c^3,\]then
\[a^2+b^2-c^2 \gt 6(c-a)(c-b).\]You can prove this by way of a counter-example:

Let
\[a=0.\]We then see that
\[b^3=c^3,\]\[b=c.\]Consequently,
\[b^2-c^2 \gt 6(c-a)(c-b),\]\[b^2-b^2 \gt 6c(c-b),\]\[0 \gt 6b(b-b),\]\[0 \gt 0,\]and we have encountered a contradiction. Therefore, the conclusion is false. QED

Answer 14

@ across
"Let a,b,c be positive real "