\(x^2+y^2-x^2y^2+xy-x-y\)

\(=x^2-x^2y^2+y^2-y+xy-x\)

\(=x^2\left(1-y^2\right)+y\left(y-1\right)+x\left(y-1\right)\)

\(=x^2\left(1-y\right)\left(y+1\right)+y\left(y-1\right)+x\left(y-1\right)\)

\(=\left(y-1\right)\left[-x^2\left(y+1\right)+y-x\right]\)

\(=\left(y-1\right)\left[-x^2y-x^2+y-x\right]\)

Ngại viết đặt cho nhanh :>

\(a^2-2a+b^2+4b+4c^2-4c+6\)

\(=\left(a^2-2a+1\right)+\left(b^2+4b+4\right)+\left(4c^2-4c+1\right)\)

\(=\left(a-1\right)^2+\left(b+2\right)^2+\left(2c+1\right)^2\)(*)

Ta có : (*) \(\ge0\)

Dấu ''='' xảy ra <=> \(a=1;b=-2;c=-\frac{1}{2}\)(**)

Vậy GTNN biểu thức là 0 <=> ta có (**) 

tìm giá trị nhỏ nhất giúp ạ

Ta có : \(^{4x^2}\)+ \(\frac{1}{x^2}\)+ \(7\)\(=\)\(8x\)+ \(\frac{4}{x}\)

\(\Rightarrow\) \(4x^4\)+ \(1\)+ \(7x^2\)\(=\)\(8x^3\)+ \(4x\)

\(\Rightarrow\) \(4x^4\)- \(8x^3\)+ \(7x^2\)-\(4x\)+\(1\)\(=\)\(0\)

\(\Rightarrow\) 4x³(x-1) - 4x²(x-1) + 3x(x-1) - (x-1) = 0

\(\Rightarrow\) (x-1) ( 4x³ -4x² +3x -1) = 0

\(\Rightarrow\) (x-1) [2x²(2x-1) - x(2x-1) + (2x-1)] = 0

\(\Rightarrow\) (x-1) (2x-1) (2x² - x +1) = 0

\(\Rightarrow\) (x-1) (2x-1) [ 2(x-\(\frac{1}{4}\))² + \(\frac{7}{8}\)] = 0

Dễ thấy : 2(x-\(\frac{1}{4}\))² + \(\frac{7}{8}\)> 0 \(\forall x\)

\(\Rightarrow\) \(\orbr{\begin{cases}x-1=0\\2x-1=0\end{cases}}\)

\(\Rightarrow\)\(\orbr{\begin{cases}x=1\\x=\frac{1}{2}\end{cases}}\)

Vậy \(x\in\){1;\(\frac{1}{2}\)}

Ta có:

Do nên

=>      

=>  

=>  

\(\left(x+3\right)^2=9\left(2x-1\right)^2\)

\(\Leftrightarrow x^2+6x+9=9\left(4x^2-4x+1\right)\)

\(\Leftrightarrow x^2+6x+9=36x^2-36x+9\)

\(\Leftrightarrow x^2+6x+9-36x^2+36x-9=0\)

\(\Leftrightarrow-35x^2+42x=0\)

\(\Leftrightarrow-7x\left(5x-6\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}-7x=0\\5x-6=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{6}{5}\end{cases}}}\)

\(\left(x+3\right)^2=9\left(2x-1\right)^2\)

\(\Leftrightarrow x^2+6x+9=9\left(4x^2-4x+1\right)\)

\(\Leftrightarrow x^2+6x+9=36x^2-36x+9\)

\(\Leftrightarrow-35x^2+42x=0\)

\(\Leftrightarrow-7x\left(5x-6\right)=0\Leftrightarrow x=0;\frac{6}{5}\)