\(\sqrt{3}\sin^2\left(x\right)+\frac{1}{2}\sin2x=\tan2x\)\(\text{​​}\sqrt{3}\sin^2\left(x\right)+\frac{1}{2}\sin2x=\tan2x\)

\(2x^2-4x+3=\left(4x-3\right)\sqrt{x^2-x+1}\)

\(\sqrt{1-x}+\sqrt{1+x}=2-\frac{x^2}{4}\)

\(3\sqrt{5x+1}-3\sqrt{4-x}-3x^2+5x+3=0\)

\(\sqrt{x+1}+1=4x^2+\sqrt{3x}\)

tìm m để hệ phương trình sau có nghiệm:

a,\(\left\{{}\begin{matrix}\sqrt{x+1}+\sqrt{y-1}=m\\x+y=m^2-4m+6\end{matrix}\right.\)

b,\(\left\{{}\begin{matrix}2x+\sqrt{y-1}=m\\2y+\sqrt{x-1}=m\end{matrix}\right.\)

\(x+\sqrt{4-x^2}=2+3x\sqrt{4-x^2}\)

\(\sqrt{4x-1}+\sqrt{4x^2-1}=1\)

Giải phương trình : x²+³\(\sqrt{x^4-x^2}\) =2x+1

Cho a>0. tìm Min của: P= \(\dfrac{a^2+1}{a}+\dfrac{a}{a^2+1}\)