Đáp án + Giải thích các bước giải:
`F=\frac{a^2b^(1/2)+a^(1/2)b^2}{sqrt(a^3)+sqrt(b^3)}`
`=(a^2b^2(b^(-3/2)+a^(-3/2)))/(sqrt(a^3)+sqrt(b^3))`
`=(a^2b^2(1/(sqrt(b^3))+1/sqrt(a^3)))/(sqrt(a^3)+sqrt(b^3))`
`=(a^2b^2(sqrt(a^3)+sqrt(b^3)))/((sqrt(a^3)+sqrt(b^3))(sqrt(a^3).sqrt(b^3))`
`=(a^2b^2)/(sqrt(a^3).sqrt(b^3))`
`=(a^2b^2)/(a^(3/2)b^(3/2))=a^(1/2)b^(1/2)=sqrt(ab)` `(a,b>0)`
`G=frac{(\root{4}{a^3b^2})^4}{\root{3}{sqrt(a^12b^6)}}`
`=\frac{((a^3b^2)^(1/4))^4}{\root{3}((a^12b^6)^(1/2)}`
`=\frac{(a^3b^2)^(1/4. 4)}{\root{3}(a^6b^3}`
`=(a^3b^2)/((a^6b^3)^(1/3))`
`=(a^3b^2)/(a^2b)=ab` `(a,b>0)`
