3sin^4 x +2cos^4 x= 98/81 (*)
tính A= 2sin^4 x + 3cos^4 x
Giải:
Từ(*) [TEX]\Rightarrow 2sin^{4}(x) + 2cos^{4}(x)= \frac{98}{81}-sin^{4}(x)[/TEX]
[TEX]\Rightarrow A= \frac{98}{81}-sin^{4}(x) + cos^{4}(x)=\frac{98}{81} + cos2x[/TEX]
[TEX](*)\Leftrightarrow 3(\frac{1-cos2x}{2})^2+2(\frac{1+cos2x}{2})^2=\frac{98}{81}[/TEX]
Đặt:[TEX]\left{\begin{\frac{1-cos2x}{2}=a}\\{\frac{1+cos2x}{2}=b}[/TEX]
Ta có:[TEX]\left{\begin{3a^2 + 2b^2=\frac{98}{81}}\\{a+b=1} \Leftrightarrow\left{\begin{3a^2+2(1-a)^2=\frac{98}{81}}\\{b=1-a}[/TEX]
[TEX]\Rightarrow3a^2+2(a^2-2a+1)=\frac{98}{81}[/TEX]
[TEX]\Leftrightarrow 405a^2-324x+64=0[/TEX]
[TEX]\left[\begin{a=\frac{4}{9}}\\{a=\frac{16}{25}}[/TEX]
\Leftrightarrow[TEX]\left[\begin{cos2x=\frac{1}{9}}\\{cos2x = \frac{-7}{25}} [/TEX]
Thay lần lượt các gt của cos2x vào:[TEX]A=\frac{98}{81} + cos2x[/TEX]
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