((9*(3^0.5)+5*(11^0.5))⼀6*(3^0.5))^(1⼀3)+((9*(3^0.5)-5*(11^0.5))⼀6*(3^0.5))^(1⼀3)= ? 要写过程 !

不能用计算器
2025-01-04 00:27:09
推荐回答(1个)
回答1:

((9*(3^0.5)+5*(11^0.5))/6*(3^0.5))^(1/3)+((9*(3^0.5)-5*(11^0.5))/6*(3^0.5))^(1/3)
解:设3^0.5=a 11^0.5=b
原式= (9a+5b)/6*a^(1/3)+(9a-5b)/6*a^(1/3)
= [(9a+5b)/6+(9a-5b)/6]*a^(1/3)
=3a*a^(1/3)=3a^(4/3)=3*3^(2/3)=3*三次根号9