完全立方公式[ (x-y)^3 × (√x+√y)^(-3) + 3(x√y-y√x) ] / (x√x+y√y)
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完全立方公式
[ (x-y)^3 × (√x+√y)^(-3) + 3(x√y-y√x) ] / (x√x+y√y) =[ (√x-√y)^3 + 3√xy × (√x-√y) ] / (x√x+y√y) =(x√x-y√y) / (x√x+y√y)什么意思,没看明白
[ (x-y)^3 × (√x+√y)^(-3) + 3(x√y-y√x) ] / (x√x+y√y) =[ (√x-√y)^3 + 3√xy × (√x-√y) ] / (x√x+y√y) =(x√x-y√y) / (x√x+y√y)什么意思,没看明白
[ (x-y)^3 × (√x+√y)^(-3) + 3(x√y-y√x) ] / (x√x+y√y)
=[ (x-y)^3 /(√x+√y)^3 + 3√(xy) × (√x-√y) ] / (x√x+y√y) (注:中括弧中第2项提取√(xy) )
={ [(x-y)/(√x+√y)]^3 + 3√(xy) × (√x-√y) } / (x√x+y√y) (注:第1项中x-y因式分解(√x+√y)(√x-√y) )
=[ (√x-√y)^3 + 3√xy × (√x-√y) ] / (x√x+y√y) (注:把第1项用完全立方展开,再合并整理)
=(x√x-y√y) / (x√x+y√y)
=[ (x-y)^3 /(√x+√y)^3 + 3√(xy) × (√x-√y) ] / (x√x+y√y) (注:中括弧中第2项提取√(xy) )
={ [(x-y)/(√x+√y)]^3 + 3√(xy) × (√x-√y) } / (x√x+y√y) (注:第1项中x-y因式分解(√x+√y)(√x-√y) )
=[ (√x-√y)^3 + 3√xy × (√x-√y) ] / (x√x+y√y) (注:把第1项用完全立方展开,再合并整理)
=(x√x-y√y) / (x√x+y√y)
[ (x-y)^3 × (√x+√y)^(-3) + 3(x√y-y√x) ] / (x√x+y√y)
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