\(x^2-\text{5}xy-14y^2\)

\(=x^2+2xy-7xy-14y^2\)

\(=x\left(x+2y\right)-7y\left(x+2y\right)\)

\(=\left(x+2y\right)\left(x-7y\right)\)

a) \(x^2-5xy-14y^2=x^2-7xy+2xy-14y^2\)

\(=\left(x-7y\right)\left(x+2y\right)\)

b) \(x^2-5x+6=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\)

c) \(x^4+4=x^4+4x^2+4-\left(2x\right)^2\)

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

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

d) 

\(4x\left(x-y\right)+3\left(y-x\right)^2\)

\(=4x\left(x-y\right)+3\left(x-y\right)\left(x-y\right)\)

\(=\left(x-y\right)\left[4x+3\left(x-y\right)\right]\)

\(=\left(x-y\right)\left(4x+3x-3y\right)\)

\(4x\left(x-y\right)+3\left(y-x\right)^2\)

\(=\)\(4x\left(x-y\right)+3\left(x-y\right)^2\)

\(=\)\(4x\left(x-y\right)+\left(3x-3y\right)\left(x-y\right)\)

\(=\)\(\left(x-y\right)\left(4x+3x-3y\right)\)

\(=\)\(\left(x-y\right)\left(7x-3y\right)\)

Chúc bạn học tốt ~ 

\(C=2x^2-5x-7\)

   \(=2\left(x^2-\frac{5}{2}x-\frac{7}{2}\right)\)

   \(=2\left[x^2-2.x.\frac{5}{4}+\frac{25}{16}-\frac{81}{16}\right]\)

    \(=2\left[\left(x-\frac{5}{4}\right)^2-\frac{81}{16}\right]\)

    \(=2\left(x-\frac{5}{4}\right)^2-\frac{81}{8}\ge-\frac{81}{8}\forall x\)

Dấu "=" xảy ra khi \(x=\frac{5}{4}\)

Vậy GTNN của C là \(-\frac{81}{8}\)khi \(x=\frac{5}{4}\)

Bài này bạn phải học khoảng 2 đến 3 tuần rồi chứ nhỉ

Chúc bạn học tốt.

\(C=2x^2-5x-7\)

\(C=x^2-2\cdot x\cdot\frac{5}{2}+\left(\frac{5}{2}\right)^2-13,25+x^2\)

\(C=\left(x-\frac{5}{2}\right)^2+x^2-13,25\)

\(C\ge13,25\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x-\frac{5}{2}=0\\x=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{5}{2}\\x=0\end{cases}}\)

Vậy,.......