1. 2a^{2}b^{2}+2b^{2}c^{2}+2c^{2}a^{2}-a^{4}-b^{4}-c^{4}^{ }2. a^{3}+1/a^{3}=18*3^{1/2 },prove that, x = 3^{1/2 }+ 2^{1/2}

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- Feb 13th 2013, 11:36 AMrizwmunresolve into factor
1. 2a

^{2}b^{2}+2b^{2}c^{2}+2c^{2}a^{2}-a^{4}-b^{4}-c^{4}^{ }2. a^{3}+1/a^{3}=18*3^{1/2 },prove that, x = 3^{1/2 }+ 2^{1/2} - Feb 13th 2013, 01:44 PMSorobanRe: resolve into factor
Hello, rizwmun!

Quote:

Quote:

Therefore: .

- Feb 14th 2013, 11:23 AMrizwmunRe: resolve into factor
thanks for replay.....but for nunmer 2, I have to prove the last portion from first portion not by last portion.

And I need whole procedure for number 1. - Feb 14th 2013, 04:56 PMSorobanRe: resolve into factor
Hello agaibn, rizwmun!

I have a method for #2 ... which is a bit devious.

Perhaps someone else can find an elegant solution.

Quote:

. . .

Let

Cube both sides: .

. . . . .

. . . . .

From [1], we have: .

We find that the only real root is:.

Substitute into [2]: .

Quadratic Formula: .

. . . . . . . . . . . . . . .

Therefore: .

- Feb 15th 2013, 10:38 PMRolandoGambleRe: resolve into factor
thanks for replay.....but for nunmer 2, I have to prove the last portion from first portion not by last portion.

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