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a) 4x*(x+y)*(x+y+z)*(x+z)+y^2+z^2
=4*x*y*z^2+4*x^2*z^2+z^2+4*x*y^2*z+12*x^2*y*z+8*x^3*z+4*x^2*y^2+y^2+8*x^3*y+4*x^4
b) x^3-19x-30
=(x-5)*(x+2)*(x+3)
\(A=\dfrac{\dfrac{1}{9}:\dfrac{7}{5}:\dfrac{4}{3}}{\dfrac{1}{81}:\dfrac{49}{25}:\dfrac{16}{9}}=\dfrac{5}{84}:\dfrac{25}{7056}=\dfrac{84}{5}\)
bài 3:
b) \(x^2-2x+5+y^2-4y=0\)
\(\Leftrightarrow x^2-2x+1+y^2-4y+4=0\)
\(\Leftrightarrow\left(x-1\right)^2+\left(y-2\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\y-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)
Vậy x=1; y=2
c) \(x^2+4y^2+13-6x-8y=0\)
\(\Leftrightarrow x^2-6x+9+4y^2-8y+4=0\)
\(\Leftrightarrow\left(x-3\right)^2+\left(2y-2\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\2y-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\2y=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)
Vây x=3; y=1
Bài 3:
a) \(x\left(x+4\right)-5\left(x-4\right)=0\)
\(\Leftrightarrow x^2+4x-5x+20=0\)
\(\Leftrightarrow x^2-x+20=0\)
\(\Leftrightarrow x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}+20=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2+\dfrac{79}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=\dfrac{-79}{4}\)
\(\Rightarrow\) ptvn
\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{2013}=\frac{1}{x+y+z}\Rightarrow\frac{yz+xz+xy}{xyz}=\frac{1}{x+y+z}\Rightarrow\left(yz+xz+xy\right)\left(x+y+z\right)=xyz\)
\(\Rightarrow y^2z+yz^2+x^2z+xz^2+x^2y+xy^2+2xyz+xyz=xyz\)
\(\Rightarrow y^2z+yz^2+x^2z+xz^2+x^2y+xy^2+2xyz=0\)
\(\Rightarrow\left(x^2y+x^2z+xy^2+xyz\right)+\left(y^2z+xz^2+y^2z+xyz\right)=0\)
\(\Rightarrow x\left(xy+xz+y^2+yz\right)+z\left(yz+xz+y^2+xy\right)=0\)
\(\Rightarrow\left(x+z\right)\left(xy+xz+y^2+yz\right)=\left(x+z\right)\left(x\left(y+z\right)+y\left(y+z\right)\right)=\left(x+y\right)\left(y+z\right)\left(x+z\right)=0\)
\(\Rightarrow\hept{\begin{cases}x+y=0\Rightarrow x^3+y^3=0\\y+z=0\Rightarrow y^5+z^5=0\\x+z=0\Rightarrow z^7+x^7=0\end{cases}}\)
\(\Rightarrow A=\left(x^3+y^3\right)\left(y^5+z^5\right)\left(z^7+x^7\right)=0\)