giải phương trình: $\sqrt{x}+\sqrt[3]{x+8}-\sqrt{x+8}=0$

Giải hệ phương trinh sau:

$\left\{\begin{matrix}
 \left ( \sqrt[3]{15x^6-9y^4+7y^2-16x+4} \right )^{2013}+\left ( \sqrt[4]{20y^6-8x^2+7x^2-17y-2} \right )^{2014}= \left ( \sqrt[5]{5x^6+6x^5-4y^6-3y^3-3y-4+3}\right )^{2015} & \\
 9\left (x^{10}-10x^9+50x^8-160x^7+360x^6-592x^5+719x^4-636x^3+392x^2-152x+31  \right )\left ( 81x^5-270y^4+360y^3-243y^2+84y-11 \right )^2=x^6-6x^5+18x^4y+6x^4-72x^3y+16x^3+108x^2y^2-12x^2-216xy^2+144xy-24x+216y^3-21y^2+72y-8&
\end{matrix}\right.$

 

P/s: vì đề hơi dài, nên sẽ khó nhìn, mong mọi người thông cảm ạ!!!!!

$\left\{\begin{matrix}\sqrt[5]{4x^5+y^5}+\sqrt[4]{3x^4+2y^4}+\sqrt[3]{2x^3+3y^3}+\sqrt{x^2+4y^2}=\sqrt[6]{6}& \\ 2\sqrt[2013]{\frac{3x^6-12x^5y+30x^4y^2-40x^3y^3+30x^2y^4-12xy^5+2y^6}{-x^6+8x^5y-19x^4y^2+20x^3y^3-10x^2y^4+2xy^5}}=3\left(\frac{3x^2-4xy+2y^2}{y^2-x^2} \right)^{\frac{2014}{2015}}-1 & \end{matrix}\right.$

$\left\{\begin{matrix} \sqrt[4]{3y^6-2y^5+y^4+x^6+x^5-3y^4}+\sqrt[3]{4x^2-2y^2+6xy^2}=3 & \\ x^3(2y-x)(x^2+y^2)=6x^3y-3x^4-1& \end{matrix}\right.$

cho 3 số x;y;z>0. CMR:

 

$\prod \left ( \frac{x+y}{y+z}+\frac{y+z}{x+y} \right )
\geq \frac{(x+y)^2(y+z)^2(z+x)^2}{8x^2y^2z^2}$

$\frac{1}{2x-5}+\frac{1}{x-4}+\frac{1}{3x-6}=\frac{7x^2-44x+73}{11x^3-96x^2+294x-317}+\frac{28x^2-116x+124}{82x^3-498x^2+1020x-712}$$+\frac{21x^2-96x+111}{51x^3-342x^2+774x-591}$


phương trình có 1 nghiệm duy nhất x=1

cho x;y;z$\epsilon z^+; x\geq z$

 

$\left ( \frac{2x-3}{14x-41} \right )^{\sqrt{2013}}+\left ( \frac{7x-23}{19-x} \right )^{\sqrt{2013}}+\left ( \frac{x+1}{17x-53} \right )^{\sqrt{2013}}$=$3^{1-\sqrt{2013}}$