Giải thích các bước giải:
Áp dụng bđt Svacxo ta có :
$\dfrac{\sin^4\alpha}{a}+\dfrac{\cos^4\alpha}{b}\ge \dfrac{(\sin^2\alpha+\cos^2\alpha)^2}{a+b}=\dfrac{1}{a+b}$
Dấu = xảy ra khi $\dfrac{\sin^2\alpha}{a}=\dfrac{\cos^2\alpha}{b}=\dfrac{1}{2(a+b)}$
$\rightarrow A=(\dfrac{\sin^2\alpha}{a})^3+(\dfrac{\cos^2\alpha}{b})^3$
$\rightarrow A=(\dfrac{1}{2(a+b)})^3+(\dfrac{1}{2(a+b)})^3=\dfrac{1}{4(a+b)^3}$