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}
Hello agaibn, rizwmun!
I have a method for #2 ... which is a bit devious.
Perhaps someone else can find an elegant solution.
. . .
Let
Cube both sides: .
. . . . .
. . . . .
From [1], we have: .
We find that the only real root is:.
Substitute into [2]: .
Quadratic Formula: .
. . . . . . . . . . . . . . .
Therefore: .
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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