\(A=\left[\dfrac{\left(a-1\right)^2}{a^2+a+1}+\dfrac{2a^2-4a-1}{\left(a-1\right)\left(a^2+a+1\right)}+\dfrac{1}{a-1}\right]\cdot\dfrac{a\left(a^2+1\right)}{2a}\)
\(=\dfrac{a^3-3a^2+3a-1+2a^2-4a-1+a^2+a+1}{\left(a-1\right)\left(a^2+a+1\right)}\cdot\dfrac{a^2+1}{2}\)
\(=\dfrac{a^3-1}{\left(a-1\right)\left(a^2+a+1\right)}\cdot\dfrac{a^2+1}{2}=\dfrac{a^2+1}{2}\)
giải hệ phương trình:
a,\(\left\{{}\begin{matrix}\dfrac{1}{2}\left(x+2\right)\left(y+3\right)=\dfrac{1}{2}xy+50\\\dfrac{1}{2}\left(x-2\right)\left(y-2\right)=\dfrac{1}{2}xy-32\end{matrix}\right.\)
b,\(\left\{{}\begin{matrix}\dfrac{-1}{2}x+\dfrac{1}{3}y=0\\y-x=1\end{matrix}\right.\)
c,\(\left\{{}\begin{matrix}x\left(y-2\right)=\left(x+2\right)\left(y-4\right)\\\left(x-3\right)\left(2y+7\right)=\left(2x-7\right)\left(y+3\right)\end{matrix}\right.\)
cho a,b,c là các số dơng thỏa mãn:\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\le3\)
chứng minh: \(\dfrac{a}{1+b^2}+\dfrac{b}{1+c^2}+\dfrac{c}{1+a^2}+\dfrac{1}{2}\left(ab+bc+ca\right)\ge3\)
\(\left\{{}\begin{matrix}5y-5x=xy\\\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{4}{5}\\\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{1}{2x-3y}+\dfrac{5}{3x+y}=\dfrac{5}{8}\\\dfrac{3}{2x-3y}-\dfrac{5}{3x+y}=-\dfrac{3}{8}\\\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x-y=2\\y-3z=2\\-3x-2y+z=-2\end{matrix}\right.\)
Cho a,b>0 với \(\dfrac{1}{a}+\dfrac{1}{c}=\dfrac{2}{b}\), chứng minh \(\dfrac{a+b}{2a-b}+\dfrac{c+b}{2c-b}\ge4\)
Sd bđt Cauchy nha!
Tìm x :
a, \(\left(2x+\dfrac{1}{2}\right)^2-\left(1-2x\right)^2=0\)
b, \(x.\left(x-2\right)+2-x=0\)
\(A=\sqrt{\dfrac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)
Tìm giá trị nguyên của x để A là 1 số nguyên
Tìm MIN:
\(G=\dfrac{1}{2}\left(\dfrac{x^{10}}{y^2}+\dfrac{y^{10}}{x^2}\right)+\dfrac{1}{4}\left(x^{16}+y^{16}\right)-\left(1+x^2y^2\right)^2\)
giai he phuongtrinh \(\left\{{}\begin{matrix}x^2+\dfrac{1}{y^2}+\dfrac{x}{y}=3\\x+\dfrac{1}{y}+\dfrac{x}{y}=3\end{matrix}\right.\)
a) Giải hệ phương trình: \(\left\{{}\begin{matrix}\dfrac{3x}{x+1}-\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
b)Giải phương trình: \(\sqrt[3]{2+x}+\sqrt[3]{5-x}=1\)
c) Cho a, b, c > 0 thỏa mãn biểu thức a+b+c=1
Chứng minh rằng: \(\sqrt{a+bc}+\sqrt{b+ac}+\sqrt{c+ab}\le2\)
Mn giúp mình với ạ, mk cần gấp lắm a~. Cảm ơn mn nhiều
