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设2008x3=2009y3=2010z3,xyz>0,且3√(2008x2+2009y2+2010z2)=3√2008+3√2009+3√2010,求x分之1+y分之1+z分之1的值

题目详情
设2008x3=2009y3=2010z3,xyz>0,且3√(2008x2+2009y2+2010z2)=3√2008+3√2009+3√2010,求x分之1+y分之1+z分之1的值
▼优质解答
答案和解析
设2008x^3=2009y^3=2010z^3 = k^3那么3√2008 = k/x3√2009 = k/y3√2010 = k/z2008x2+2009y2+2010z2 = k^3/x+ k^3/y + k^3/z = k^3(1/x+1/y+1/z)所以3√(2008x2+2009y2+2010z2) = k 3√(1/x+1/y+1/z) = 3√2008+3...