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+

问题描述:

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?