\(P=sin^{10}x+cos^{10}x-\dfrac{sin^6x+cos^6x}{sin^22x+4cos^22x}\)
\(=sin^{10}x+cos^{10}x-\dfrac{\left(sin^2x+cos^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)}{4-3sin^22x}\)
\(=sin^{10}x+cos^{10}x-\dfrac{1-\dfrac{3}{4}sin^22x}{4-3sin^22x}\)
\(=sin^{10}x+cos^{10}x-\dfrac{1}{4}\)
\(\le sin^2x+cos^2x-\dfrac{1}{4}=\dfrac{3}{4}\)
\(maxP=\dfrac{3}{4}\Leftrightarrow\left\{{}\begin{matrix}sin^{10}x=sin^2x\\cos^{10}x=cos^2x\end{matrix}\right.\Leftrightarrow x=\dfrac{k\pi}{2}\)
Đúng 0
Bình luận (0)
