1.Cho x;y;z>0 thoã mãn: $x+y+z+\sqrt{xyz}=4$. Tính: P=$\sqrt{x(4-y)(4-z)}+\sqrt{y(4-x)(4-z)}+\sqrt{z(4-y)(4-x)}-\sqrt{xyz}$
2. Cho a;b thoả mãn b>$\frac{a^2}{4}$. CMR: $\sqrt[3]{\frac{ab+\sqrt{a^2b^2-\frac{4}{27}(a^2-b)^3}}{2}}+\sqrt[3]{\frac{ab-\sqrt{a^2b^2-\frac{4}{27}(a^2-b)^3}}{2}}=a$
3. Cho $\frac{bc}{a}+\frac{ca}{b}+\frac{ab}{c}=a+b+c$. Tính P=$\frac{a^2+b^2}{(a+c)(b+c)}+\frac{b^2+c^2}{(b+a)(c+a)}+\frac{c^2+a^2}{(c+b)(a+b)}$
4. Cho x=$\sqrt{2}+\sqrt[3]{3}$. Tính P=$x^{2013}-6x^{2011}-6x^{2010}+12x^{2009}-36x^{2008}+x^{2007}+2013$