Question

Answer 1

Pt\(\Leftrightarrow2y.cosx-y.sinx+4y=cosx+2sinx+3\)

\(\Leftrightarrow sinx\left(-y-2\right)+cosx\left(2y-1\right)=3-4y\) (1)

Phương trình (1) có nghiệm 

\(\Leftrightarrow\left(-y-2\right)^2+\left(2y-1\right)^2\ge\left(3-4y\right)^2\)

\(\Leftrightarrow5y^2+5\ge9-24y+16y^2\)

\(\Leftrightarrow11y^2-24y+4\le0\)

\(\Leftrightarrow\dfrac{2}{11}\le y\le2\)

\(\Rightarrow y_{min}=\dfrac{2}{11}\)

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