=\(\frac{\left(e^2-2e.m+m^2-e^2-2e.m-m^2\right).\left(y^2-2y+1-y^2-2y-1\right)}{a.16.n.h}.\frac{e}{u^{-1}}\)
= \(\frac{-4e.m.\left(-4y\right)}{a.16.n.h}.\frac{e}{u^{-1}}\)
=\(\frac{16e.m.y}{16a.n.h}.\frac{e}{\frac{1}{4}}\)
=\(\frac{e.m.y}{a.n.h}.e.u=\frac{e.m.y.e.u}{a.n.h}\)
a) gpt \(\left(x-1\right)\left(x+2\right)+4\left(x-1\right)\sqrt{\frac{x+2}{x-1}}=12\)
b) ghpt \(\left\{\begin{matrix}2\sqrt{x}\left(1+\frac{1}{x+y}\right)=3\\2\sqrt{y}\left(1-\frac{1}{x+y}\right)=1\end{matrix}\right.\)
Cho \(x,y,z\in\left[0;2\right]\) . Tìm GTLN của biểu thức
\(P=\frac{1}{8}\left[\left(2-x\right)\left(2-y\right)\left(4-z\right)+\frac{8x}{y+z+2}+\frac{8y}{z+x+2}+\frac{8z}{x+y+2}\right]\)
1) 0<a,b,c<1 và ab+bc+ca=1.find Min of:
\(M=\frac{a^2\left(1-2b\right)}{b}+\frac{b^2\left(1-2c\right)}{c}+\frac{c^2\left(1-2a\right)}{a}\)
2) a,b,c>0.CMR:
\(\frac{1}{\left(2a+b\right)^2}+\frac{1}{\left(2b+c\right)^2}+\frac{1}{\left(2c+a\right)^2}\ge\frac{1}{ab+bc+ca}\)
3)a,b,c>0 CMR:
\(\left(\frac{a}{a+b}\right)^2+\left(\frac{b}{b+c}\right)^2+\left(\frac{c}{c+a}\right)^2\ge\frac{1}{2}\left(\frac{b}{a+b}+\frac{c}{b+c}+\frac{a}{c+a}\right)\)
Giải hệ:
\(\left\{\begin{matrix}\frac{\left(a+5\right)\left(b+2\right)}{2}=\frac{ab}{2}+45\\\frac{\left(a-1\right)\left(b-1\right)}{2}=\frac{ab}{2}-15\end{matrix}\right.\)
Cho a,b thỏa ab=1; a+b\(\ne\) 0 Tính
\(P=\frac{1}{\left(a+b\right)^3}\left(\frac{1}{a^3}+\frac{1}{b^3}\right)+\frac{1}{\left(a+b\right)^4}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)+\frac{6}{\left(a+b\right)^5}\left(\frac{1}{a}+\frac{1}{b}\right)\)
cho x,y,z \(\ge0\)và đôi một khác nhau t/m (x+z)(y+z)=1
chứng ming :\(\frac{1}{\left(x-y\right)^2}+\frac{1}{\left(x+z\right)^2}+\frac{1}{\left(y+z\right)^2}\ge4\)
Help me vs
\(\frac{2.1+1}{\left(1+1\right)^2}+\frac{2.2+1}{\left(2^2+2\right)^2}+\frac{2.3+1}{\left(3^3+3\right)^2}+....+\frac{2.2015+1}{\left(2015^2+2015\right)^2}+\frac{2.1016+1}{\left(2016^2+2016\right)^2}\)
tính tổng . ai giúp vs
Chứng minh :
\(\left(\frac{a^2}{b^2}\right)+\left(\frac{b^2}{c^2}\right)+\left(\frac{c^2}{a^2}\right)\ge\left(\frac{c}{b}\right)+\left(\frac{b}{a}\right)+\left(\frac{a}{c}\right)\)
\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{1000}\right)\)
