更新1:
我想問 c 的 substitution 應該係咩? a, b 我都諗到
更新2:
岩哂啊! 但我都係唔知 c = 2x + 8√2 - 12√3 係點觀察出黎, 係要爆開一d野先, 定....? a = x - 2√2 + 5√3, b = -3x - 6√2 + 7√3 都好容易見到
更新3:
明左.. thx 幫埋我呢條啊, thx
回答 ()
2012-03-07 8:07 am
✔ 最佳答案
(a) a + b + c = 0 => a = -(b + c)a^3 + b^3 + c^3 + 3abc
= -(b + c)^3 + b^3 + c^3 - 3bc(b + c)
= -(b^3 + 3bc(b + c) + c^3) + b^3 + c^3 - 3bc(b + c)
= 0
(b) Consider a = x - 2√2 + 5√3, b = -3x - 6√2 + 7√3, c = 2x + 8√2 - 12√3a + b + c
= x - 2√2 + 5√3 -3x - 6√2 + 7√3 + 2x + 8√2 - 12√3
= -2√2 + 5√3 - 6√2 + 7√3 + 8√2 - 12√3
= 0
So, the original equation become
3abc = 0
3(x - 2√2 + 5√3)(-3x - 6√2 + 7√3)(2x + 8√2 - 12√3) = 0
x = 2√2 - 5√3, (7√3 - 6√2)/3, 6√3 - 4√2
2012-03-09 3:02 am
thz Kenneth
2012-03-07 8:22 am
[8^(1/3) = 2]
c^3 = 8(x + 4√2 - 6√3)^3
= 2^3 x ( x + 4√2 - 6√3 )^3
= [ 2 ( x + 4√2 - 6√3 ) ] ^3 <---- law of index, a^m x b^m = (ab)^m
= (2x + 8√2 - 12√3) ^3
c^3 = 8(x + 4√2 - 6√3)^3
= 2^3 x ( x + 4√2 - 6√3 )^3
= [ 2 ( x + 4√2 - 6√3 ) ] ^3 <---- law of index, a^m x b^m = (ab)^m
= (2x + 8√2 - 12√3) ^3
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