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17 tháng 2 2017

Giá trị A bằng 0 khi 2.x -1 =0

                           <=> 2.x=1

                           <=> x=1/2

5 tháng 9 2016

a/ \(A=\left(x+1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)=\left[\left(x+1\right)\left(x-6\right)\right].\left[\left(x-2\right)\left(x-3\right)\right]\)

\(=\left(x^2-5x-6\right)\left(x^2-5x+6\right)=\left(x^2-5x\right)^2-36\ge-36\)

Suy ra Min A = -36 <=> \(x^2-5x=0\Leftrightarrow x\left(x-5\right)=0\) \(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=5\end{array}\right.\)

b/ \(B=19-6x-9x^2=-9\left(x-\frac{1}{3}\right)^2+20\le20\)

Suy ra Min B = 20 <=> x = 1/3

5 tháng 9 2016

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

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

\(\left(x^2-5x-6\right)\left(x^2-5x+6\right)=\left(x^2-5x\right)^2-36\)

Vì \(\left(x^2-5x\right)^2\ge0\)

=> \(\left(x^2-5x\right)^2-36\ge-36\)

Vậy GTNN của A là -36 khi \(x^2-5x=0\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=5\end{array}\right.\)

b) \(B=19-6x-9x^2=-\left(9x^2+6x+1\right)+20=-\left(3x+1\right)^2+20\)

Vì \(-\left(3x+1\right)^2\le0\)

=> \(-\left(3x+1\right)+20\le20\)

Vậy GTLN của B là 20 khi \(x=-\frac{1}{3}\)

1:  \(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-2\left(4x+3\right)^2+8\left(x+3\right)^2\)

\(=24x^2+2-2\left(16x^2+24x+9\right)+8\left(x^2+6x+9\right)\)

\(=24x^2+2-32x^2-48x-18+8x^2+48x+72\)

=56

2: \(=\left(4x^2+4x+1\right)\left(x-1\right)-2\left(x^3-6x^2+12x-8\right)+x\left(3-2x\right)\left(3+x\right)-\left(3x-3\right)^2\)

\(=4x^3-3x-1-2x^3+12x^2-24x+16+x\left(9-3x-2x^2\right)-\left(3x-3\right)^2\)

\(=2x^3+12x^2-27x+15+9x-3x^2-2x^3-9x^2+18x-9\)

\(=6\)

20 tháng 11 2023

1: \(C=\left(x-\dfrac{4xy}{x+y}+y\right):\left(\dfrac{x}{x+y}+\dfrac{y}{y-x}+\dfrac{2xy}{x^2-y^2}\right)\)

\(=\dfrac{\left(x+y\right)^2-4xy}{x+y}:\left(\dfrac{x}{x+y}-\dfrac{y}{x-y}+\dfrac{2xy}{\left(x-y\right)\left(x+y\right)}\right)\)

\(=\dfrac{x^2+2xy+y^2-4xy}{x+y}:\dfrac{x\left(x-y\right)-y\left(x+y\right)+2xy}{\left(x+y\right)\left(x-y\right)}\)

\(=\dfrac{x^2-2xy+y^2}{x+y}:\dfrac{x^2-xy-xy-y^2+2xy}{\left(x+y\right)\left(x-y\right)}\)

\(=\dfrac{\left(x-y\right)^2}{x+y}\cdot\dfrac{x^2-y^2}{x^2-y^2}=\dfrac{\left(x-y\right)^2}{x+y}\)

2: \(\left(x^2-y^2\right)\cdot C=-8\)

=>\(\left(x-y\right)\left(x+y\right)\cdot\dfrac{\left(x-y\right)^2}{x+y}=-8\)

=>\(\left(x-y\right)^3=-8\)

=>x-y=-2

=>x=y-2

\(M=x^2\left(x+1\right)-y^2\left(y-1\right)-3xy\left(x-y+1\right)+xy\)

\(=\left(y-2\right)^2\left(y-2+1\right)-y^2\left(y-1\right)-3xy\left(-2+1\right)+xy\)

\(=\left(y-1\right)\left[\left(y-2\right)^2-y^2\right]+3xy+xy\)

\(=\left(y-1\right)\left(-4y+4\right)+4xy\)

\(=-4\left(y-1\right)^2+4y\left(y-2\right)\)

\(=-4y^2+8y-4+4y^2-8y\)
=-4

20 tháng 11 2023

Em cảm ơn ạ.

8 tháng 7 2017

\(A=\left(2x-3\right).\left(3x^2+2x-1\right)-\left(4x+1\right)\cdot\left(x-1\right)\)

\(A=6x^3+4x^2-2x-9x^2-6x+3-\left(4x^2-4x+x-1\right)\)

\(A=6x^3+4x^2-2x-9x^2-6x+3-4x^2+4x-x+1\)

\(A=6x^3-9x^2-5x+4\)

Với \(x=\frac{1}{2}\).Ta có : 

\(A=6.\left(\frac{1}{2}\right)^3-9.\left(\frac{1}{2}\right)^2-5.\frac{1}{2}+4\)

\(A=\frac{3}{4}-\frac{9}{4}-\frac{5}{2}+4\)

\(\Rightarrow A=0\)

23 tháng 7 2017

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

\(=\left(4x^2+4x+1\right)\left(x-1\right)-2\left(x^3-6x^2+12x-8\right)+x\left(9+3x-6x-2x^2\right)-\left(9x^2-18x+9\right)\)

\(=4x^3+4x^2+x-4x^2-4x-1-2x^3+12x^2-24x+16+9x+3x^2-6x^2-2x^3-9x^2+18x+9\)

\(=\left(4x^3-2x^2-2x^3\right)+\left(4x^2-4x^2+12x^2+3x^2-6x^2-9x^2\right)+\left(x-4x-24x+9x+18x\right)+\left(-1+16+9\right)\)

\(=24\)

Vậy...........

Chúc bạn học tốt!!!

8 tháng 7 2017

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

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

\(\Rightarrow C=0\)