Sửa đa thức M(x) = 3x⁴ - 2x³ + 5x² - 4x + 1

\(P\left(x\right)=M\left(x\right)+N\left(x\right)\)

\(=3x^4-2x^3+5x^2-4x+1-3x^4+2x^3-3x^2+7x+5\)

\(=2x^2+3x+6\)

b, Tại x = -x  

< = > 2x = 0 <=> x = 0 thì giá trị của biểu thức P ( x ) = 6

Tính giá trị biểu thức là " Nhân :hay " Chia " hay " Cộng" hay Trừ " vậy .

\(M=x^4-2x^3+3x^2-2x+2\)

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

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

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

Thay  \(x^2-x=4\)vào  M ta đc:

\(M=4.\left(4+2\right)+2\)

\(=4.6+2\)

\(=26\)

M = (x^4-x^3)-(x^3-x^2)+(2x^2-2x)+2

   = x^2.(x^2-x)-x.(x^2-x)+2.(x^2-x)+2

   = (x^2-x).(x^2-x+2)+2

Thay x^2-x=4 thì :

M = 4.(4+2)+2 = 26

Tk mk nha

Em tham khảo:

a, M(\(x\) )+N(\(x\)) = 3\(x^4\) - 2\(x\)³ + 5\(x^2\) - \(4x\)+ 1 + ( -3\(x^4\) + 2\(x^3\)- 3\(x^2\)+ 7\(x\) + 5)

M(\(x\)) + N(\(x\)) = ( 3\(x^4\)- 3\(x^4\))+( -2\(x^3\) + 2\(x^3\))+(5\(x^2\) - 3\(x^2\))+( 7\(x-4x\)) +(1+5)

M(\(x\)) + N(\(x\)) = 0 + 0 + 2\(x^2\) + 3\(x\) + 6

M(\(x\)) + N(\(x\)) = 2\(x^2\) + 3\(x\) + 6

b, P(\(x\)) = M(\(x\)) + N(\(x\)) = 2\(x^2\) + 3\(x\) + 6

P(-2) = 2.(-2)² + 3.(-2) + 6 = 8 - 6 + 6 = 8 

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

\(=\dfrac{x+4x+8+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x+2\right)}{3\left(x+1\right)}\)

\(=\dfrac{6\left(x+1\right)\cdot x\left(x+2\right)}{3\left(x+1\right)\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{2x}{x-2}\)

Answer:

a) \(\frac{5x}{2x+2}+1=\frac{6}{x+1}\)

\(\Rightarrow\frac{5x}{2\left(x+1\right)}+\frac{2\left(x+1\right)}{2\left(x+1\right)}=\frac{12}{2\left(x+1\right)}\)

\(\Rightarrow5x+2x+2-12=0\)

\(\Rightarrow7x-10=0\)

\(\Rightarrow x=\frac{10}{7}\)

b) \(\frac{x^2-6}{x}=x+\frac{3}{2}\left(ĐK:x\ne0\right)\)

\(\Rightarrow x^2-6=x^2+\frac{3}{2}x\)

\(\Rightarrow\frac{3}{2}x=-6\)

\(\Rightarrow x=-4\)

c) \(\frac{3x-2}{4}\ge\frac{3x+3}{6}\)

\(\Rightarrow\frac{3\left(3x-2\right)-2\left(3x+3\right)}{12}\ge0\)

\(\Rightarrow9x-6-6x-6\ge0\)

\(\Rightarrow3x-12\ge0\)

\(\Rightarrow x\ge4\)

d) \(\left(x+1\right)^2< \left(x-1\right)^2\)

\(\Rightarrow x^2+2x+1< x^2-2x+1\)

\(\Rightarrow4x< 0\)

\(\Rightarrow x< 0\)

e) \(\frac{2x-3}{35}+\frac{x\left(x-2\right)}{7}\le\frac{x^2}{7}-\frac{2x-3}{5}\)

\(\Rightarrow\frac{2x-3+5\left(x^2-2x\right)}{35}\le\frac{5x^2-7\left(2x-3\right)}{35}\)

\(\Rightarrow2x-3+5x^2-10x\le5x^2-14x+21\)

\(\Rightarrow6x\le24\)

\(\Rightarrow x\le4\)

f) \(\frac{3x-2}{4}\le\frac{3x+3}{6}\)

\(\Rightarrow\frac{3\left(3x-2\right)-2\left(3x+3\right)}{12}\le0\)

\(\Rightarrow9x-6-6x-6\le0\)

\(\Rightarrow3x\le12\)

\(\Rightarrow x\le4\)