\(X+30\%X=-1,3\\ X=\dfrac{-1,3}{100\%+30\%}=-1\\ ---\\ X-25\%X=\dfrac{1}{2}\\ X=\dfrac{\dfrac{1}{2}}{100\%-25\%}=\dfrac{2}{3}\)

\(\left(x+1\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)=2\)

\(\Leftrightarrow x^2+4x+3-x^2-3x+10=2\)

\(\Leftrightarrow x=-11\)

x=2,5

\(\left(x-2,5\right)^4=\left(x=-2,5\right)^2\)

\(\Rightarrow\left(x-2,5\right)^6\)

\(\Rightarrow x-2,5=0\Rightarrow x=2,5\)

\(\left(x-2,5\right)^4=\left(x-2,5\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x-2,5=-1\\x-2,5=0\\x-2,5=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1,5\\x=2,5\\x=3,5\end{matrix}\right.\)

\(P=\dfrac{x^2+x+1}{\left(x-1\right)^2}\)

Điều kiện: x≠ \(1\)

Ta có:

 \(P=\dfrac{\left(x^2-2x+1\right)+\left(3x-3\right)+3}{\left(x-1\right)^2}\)

 \(=\dfrac{\left(x-1\right)^2+3\left(x-1\right)+3}{\left(x-1\right)^2}\)

\(=1+\dfrac{3}{x-1}+\dfrac{3}{\left(x-1\right)^2}\)

\(=3\left[\left(\dfrac{1}{x-1}\right)^2+2.\dfrac{1}{x-1}.\dfrac{1}{2}+\dfrac{1}{4}\right]+\dfrac{1}{4}\)

\(=3\left(\dfrac{1}{x-1}+\dfrac{1}{2}\right)^2+\dfrac{1}{4}\) ≥ \(\dfrac{1}{4}\) (Vì \(3\left(\dfrac{1}{x-1}+\dfrac{1}{2}\right)^2\text{≥}0\) )

Min P=\(\dfrac{1}{4}\) ⇔\(x=-1\)

Cho C = 0

\(\Rightarrow x+\left(-\dfrac{5}{9}\right)x^2=0\)

\(x\left(1-\dfrac{5}{9}x\right)=0\)

\(x=0\) hoặc \(1-\dfrac{5}{9}x=0\)

*) \(1-\dfrac{5}{9}x=0\)

\(\dfrac{5}{9}x=1\)

\(x=\dfrac{1}{\dfrac{5}{9}}\)

\(x=\dfrac{9}{5}\)

Vậy nghiệm của đa thức C là \(x=0;x=\dfrac{9}{5}\)

Nhân − 5 19 với x 2 . c = x − 5 19 x 2 Rút gọn x − 5 19 x 2 . Rút gọn mỗi số hạng. Bấm để xem thêm các bước... c = x − 5 x 2 19 Sắp xếp lại x và − 5 x 2 19 . c = − 5 x 2 19 + x

\(\text{Đặt }C=0\)

\(\Rightarrow x+\left(-\dfrac{5}{19}\right)x^2=0\)

\(\Rightarrow x\left(1-\dfrac{-5}{19}x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\1-\dfrac{-5}{19}x=0\Rightarrow\dfrac{-5}{19}x=1-0=1\Rightarrow x=1:\dfrac{-5}{19}=\dfrac{-19}{5}\end{matrix}\right.\)

\(\text{Vậy đa thức C có 2 nghiệm là x=0;z=}\dfrac{-19}{5}\)

Ta có: \(A=\left(x-3\right)^2+\left(11-x\right)^2\)

\(=x^2-6x+9+x^2-22x+121\)

\(=2x^2-28x+130\)

\(=2\left(x^2-14x+49+16\right)\)

\(=2\left(x-7\right)^2+32\ge32\forall x\)

Dấu '=' xảy ra khi x=7

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

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

\(=\left(x-1\right)^3-\left(x-1\right)^3\)

\(=0\)

d) \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2\)

\(=\left(x-3\right)^3-\left(x-3\right)\left(x^2+x.3+3^2\right)+6\left(x+1\right)^2\)

\(=\left(x-3\right)^3-\left(x-3\right)^3+6\left(x+1\right)^2\)

\(=0+6\left(x+1\right)^2\)

\(=6\left(x+1\right)^2\)

c. (x - 1)³ - (x - 1)(x² + x + 1)

= (x - 1)³ - (x³ - 1)

= x³ - 2x² + 2x - 1 - x³ + 1

= x³ - x³ - 2x² + 2x - 1 + 1

= -2x² + 2x

d. (x - 3)³ - (x - 3)(x² + 3x + 9) + 6(x + 1)²

= x³ - 6x² + 18x - 27 - (x³ - 27) + 6(x² + 2x + 1)

= x³ - 6x² + 18x - 27 - x³ + 27 + 6x² + 12x + 6

= x³ - x³ - 6x² + 6x² + 18x + 12x - 27 + 27 + 6

= 30x + 6

a) \(x^2-3x+8=\left(x^2-3x+\dfrac{9}{4}\right)+\dfrac{23}{4}=\left(x-\dfrac{3}{2}\right)^2+\dfrac{23}{4}\ge\dfrac{23}{4}>0\)

b) \(2x^2-2x+2=2\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{3}{2}=2\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{2}\ge\dfrac{3}{2}>0\)

a: Ta có: \(A=x^2-3x+8\)

\(=x^2-2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{23}{4}\)

\(=\left(x-\dfrac{3}{2}\right)^2+\dfrac{23}{4}>0\forall x\)

b: Ta có: \(B=2x^2-2x+2\)

\(=2\left(x^2-2\cdot x\cdot\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{4}\right)\)

\(=2\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{2}>0\forall x\)