If\( a >0\) , is\(a^{\frac{1}{3} } >a^{\frac{1}{2}}\) ?
(1)\(a^\frac{1}{2} >a\)
(2)\(a^\frac{1}{3} >a^{\frac{2}{3}}\)
Solution:
\(a^{\frac{1}{3} } >a^{\frac{1}{2}}\) ? ; given a>0
=> a^2>a^3?
=> a^2(a-1)<0?
=> a<1?
(1)\(a^\frac{1}{2} >a\) --> suff: a>a^2 => a(a-1)<0 => a>0, so a-1<0=> a<1--> answer is yes
(2)\(a^\frac{1}{3} >a^{\frac{2}{3}}\) --> suff: a>a^2 similar as (1) a <1--> answer isyes
Answer:D
...
(1)\(a^\frac{1}{2} >a\)
(2)\(a^\frac{1}{3} >a^{\frac{2}{3}}\)
Solution:
\(a^{\frac{1}{3} } >a^{\frac{1}{2}}\) ? ; given a>0
=> a^2>a^3?
=> a^2(a-1)<0?
=> a<1?
(1)\(a^\frac{1}{2} >a\) --> suff: a>a^2 => a(a-1)<0 => a>0, so a-1<0=> a<1--> answer is yes
(2)\(a^\frac{1}{3} >a^{\frac{2}{3}}\) --> suff: a>a^2 similar as (1) a <1--> answer isyes
Answer:D
...
