已知:2^x=(√10-√2)/2,2^y=(√10+√2)/2,则(x-y)+√(x³-x²y-x
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已知:2^x=(√10-√2)/2,2^y=(√10+√2)/2,则(x-y)+√(x³-x²y-xy²+y³)的值
![已知:2^x=(√10-√2)/2,2^y=(√10+√2)/2,则(x-y)+√(x³-x²y-x](/uploads/image/z/18874225-1-5.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A2%5Ex%3D%28%E2%88%9A10-%E2%88%9A2%29%2F2%2C2%5Ey%3D%28%E2%88%9A10%2B%E2%88%9A2%29%2F2%2C%E5%88%99%28x-y%29%2B%E2%88%9A%28x%26%23179%3B-x%26%23178%3By-x)
2^(X+Y)=(√10-√2)(√10+√2)/4=2;即X+Y=1
∵2^x=(√10-√2)/2x
(x-y)+√(x³-x²y-xy²+y³)=x-y+√[x²(x-y)-y²(x-y)]
=x-y+√[(x-y)(x²-y²)]=x-y+√[(x-y)²(x+y)]
=x-y+√(x-y)²=x-y+|x-y|=x-y-x+y=0
∵2^x=(√10-√2)/2x
(x-y)+√(x³-x²y-xy²+y³)=x-y+√[x²(x-y)-y²(x-y)]
=x-y+√[(x-y)(x²-y²)]=x-y+√[(x-y)²(x+y)]
=x-y+√(x-y)²=x-y+|x-y|=x-y-x+y=0
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