Question

giả sử 3.sinx^4-cosx^4=1/2 thì sinx^4+3.cosx^4=

giúp mik vs

Answer 1

Ta có hệ: \(\left\{{}\begin{matrix}3sin^4x-cos^4x=\dfrac{1}{2}\\sin^2x+cos^2x=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}3\left(1-cos^2x\right)^2-cos^4x=\dfrac{1}{2}\\sin^2x=1-cos^2x\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}4cos^4x-12cos^2x+5=0\left(1\right)\\sin^2x=1-cos^2x\left(2\right)\end{matrix}\right.\)

Từ (1) ta có: \(\Leftrightarrow\left[{}\begin{matrix}cos^2x=\dfrac{5}{2}\left(l\right)\\cos^2x=\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow sin^2x=\dfrac{1}{2}\)

\(\Rightarrow sin^4x+3cos^4x=\left(\dfrac{1}{2}\right)^2+3\left(\dfrac{1}{2}\right)^2=1\)