设2000乘以x的立方等于2001乘以y的立方也等于2002乘以z的立方,x乘y乘z大于零,3√(2000x²+2001y²+2002z²)=3√(2000)+3√(2001)+3√(2002) 求证:1÷x+1÷y+1÷z=1 (救救我!)
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![设2000乘以x的立方等于2001乘以y的立方也等于2002乘以z的立方,x乘y乘z大于零,3√(2000x²+2001y²+2002z²)=3√(2000)+3√(2001)+3√(2002) 求证:1÷x+1÷y+1÷z=1 (救救我!)](/uploads/image/z/1271845-37-5.jpg?t=%E8%AE%BE2000%E4%B9%98%E4%BB%A5x%E7%9A%84%E7%AB%8B%E6%96%B9%E7%AD%89%E4%BA%8E2001%E4%B9%98%E4%BB%A5y%E7%9A%84%E7%AB%8B%E6%96%B9%E4%B9%9F%E7%AD%89%E4%BA%8E2002%E4%B9%98%E4%BB%A5z%E7%9A%84%E7%AB%8B%E6%96%B9%2Cx%E4%B9%98y%E4%B9%98z%E5%A4%A7%E4%BA%8E%E9%9B%B6%2C3%E2%88%9A%EF%BC%882000x%26sup2%3B%2B2001y%26sup2%3B%2B2002z%26sup2%3B%29%3D3%E2%88%9A%EF%BC%882000%29%2B3%E2%88%9A%EF%BC%882001%29%2B3%E2%88%9A%EF%BC%882002%29+%E6%B1%82%E8%AF%81%EF%BC%9A1%C3%B7x%2B1%C3%B7y%2B1%C3%B7z%3D1+%28%E6%95%91%E6%95%91%E6%88%91%21%EF%BC%89)
设2000乘以x的立方等于2001乘以y的立方也等于2002乘以z的立方,x乘y乘z大于零,3√(2000x²+2001y²+2002z²)=3√(2000)+3√(2001)+3√(2002) 求证:1÷x+1÷y+1÷z=1 (救救我!)
设2000乘以x的立方等于2001乘以y的立方也等于2002乘以z的立方,x乘y乘z大于零,3√(2000x²+2001y²+2002z²)=3√(2000)+3√(2001)+3√(2002) 求证:1÷x+1÷y+1÷z=1 (救救我!)
设2000乘以x的立方等于2001乘以y的立方也等于2002乘以z的立方,x乘y乘z大于零,3√(2000x²+2001y²+2002z²)=3√(2000)+3√(2001)+3√(2002) 求证:1÷x+1÷y+1÷z=1 (救救我!)
设2000乘以x的立方等于2001乘以y的立方也等于2002乘以z的立方等于K^3 2000x²=K^3 /x 2001y²=K^3 /y 2002z²=K^3 /z
3√(2000)x=3√(2001)y=3√(2002)z=k
3√(2000)+3√(2001)+3√(2002)=k(1÷x+1÷y+1÷z)=3√(2000x²+2001y²+2002z²)=3√[K^3 (1÷x+1÷y+1÷z)]
x乘y乘z大于零
(1÷x+1÷y+1÷z)=3√(1÷x+1÷y+1÷z)
(1÷x+1÷y+1÷z)=1
明白吗?
令2000x3=2001y3=2002z3=t
3√(2000x²+2001y²+2002z²)=3√(t/x+t/y+t/z)
=3√t/x+3√t/y+3√t/z
消去3√t
3√1÷x+1÷y+1÷z=1÷x+1÷y+1÷z
x乘y乘z大于零
所以1÷x+1÷y+1÷z=1