lilolilo

$(\frac{sin2x+cos4x}{sin3x+cos3x})^{2}= 2\sqrt{2}sin(x+\frac{\pi }{4})+3$

$\left\{\begin{matrix} 6x^4-(x^3-x)y^2-(y+12)x^2=-6\\ 5x^4-(x^3-x)^2y^2-11x^2=-5 \end{matrix}\right.$

$\left\{\begin{matrix} log_{\sqrt{3}}(x+1)-log_{\sqrt{3}}(x-1)>log_{3}4\\ log_{2}(x^2-2x+5)-mlog_{x^2-2x+5}2=5 \end{matrix}\right.$

$\int_{0}^{\pi ^{2}}\sqrt{x}sin\sqrt{x}dx$

$\left\{\begin{matrix} \sqrt{x^2+y^2}+\sqrt{2xy}=8\sqrt{2}\\ \sqrt{x}+\sqrt{y}=4 \end{matrix}\right.$