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\(-4x^5\left(x^3-4x^2+7x-3\right)\)\(=-4x^8+16x^7-28x^6+12x^5\)
1. -4x( x + 3 )( x - 4 ) - 3x( x2 - x + 1 )
= -4x( x2 - x - 12 ) - 3x( x2 - x + 1 )
= -4x3 + 4x2 + 48x - 3x3 + 3x2 - 3x
= -7x3 + 7x2 + 45x
2. a) 4x( x - 5 ) - ( x - 1 )( 4x - 3 ) = 5
<=> 4x2 - 20x - ( 4x2 - 7x + 3 ) = 5
<=> 4x2 - 20x - 4x2 + 7x - 3 = 5
<=> -13x - 3 = 5
<=> -13x = 8
<=> x = -8/13
b) 6( x - 3 )( x - 4 ) - 6x( x - 2 ) = 4
<=> 6( x2 - 7x + 12 ) - 6x2 + 12x = 4
<=> 6x2 - 42x + 72 - 6x2 + 12x = 4
<=> -30x + 72 = 4
<=> -30x = -68
<=> x = 34/15
Bài 1 :
\(-4x\left(x+3\right)\left(x-4\right)-3x\left(x^2-x+1\right)\)
\(=-7x^3+7x^2+45x\)
Bài 2 :
a, \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
\(\Leftrightarrow4x^2-20x-\left[4x^2-7x+3\right]=5\)
\(\Leftrightarrow4x^2-20x-4x^2+7x-3=5\)
\(\Leftrightarrow-13x-8=0\Leftrightarrow x=-\frac{8}{13}\)
b, \(6\left(x-3\right)\left(x-4\right)-6x\left(x-2\right)=4\)
\(\Leftrightarrow6x^2-42x+72-6x^2+12x=4\)
\(\Leftrightarrow-30x+68=0\Leftrightarrow x=\frac{34}{15}\)
Bài 1 :
\(\left(x-2\right)^2-\left(x-3^2\right)=\left(x-2\right)^2-\left(x-9\right)\)
\(=x^2-4x+4-x+9=x^2-5x+13\)
Bài 2 :
a, \(P=\frac{1-4x^2}{4x^2-4x+1}=\frac{\left(1-2x\right)\left(2x+1\right)}{\left(2x-1\right)^2}\)
\(=\frac{-\left(2x-1\right)\left(2x+1\right)}{\left(2x-1\right)^2}=\frac{-\left(2x+1\right)}{2x-1}=\frac{-2x-1}{2x-1}\)
b, Thay x = -4 ta được :
\(\frac{-2.\left(-4\right)-1}{2.\left(-4\right)-1}=\frac{8-1}{-8-1}=-\frac{7}{9}\)
\(1,=-x^2+2x+15+2x^2+5x-3=x^2+7x+12\\ 2,=-4x\left(x^2-x-12\right)-3x^3+3x^2-3x\\ =-4x^3+4x^2+48x-3x^3+3x^2-3x\\ =-7x^3+7x^2+45x\)
\(a,=\left(2x-7\right)^2=\left(2.4-7\right)^2=1\)
\(b,\left(x-3\right)^3=\left(5-3\right)^3=8\)
a: \(P=\left(\dfrac{3}{2\left(x+2\right)}-\dfrac{x}{x-2}+\dfrac{2x^2+3}{\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{4\left(x-2\right)}{2x-1}\)
\(=\left(\dfrac{3\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}-\dfrac{2x\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\dfrac{4x^2+6}{2\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{4\left(x-2\right)}{2x-1}\)
\(=\dfrac{3x-6-2x^2-4x+4x^2+6}{2\left(x+2\right)\left(x-2\right)}\cdot\dfrac{4\left(x-2\right)}{2x-1}\)
\(=\dfrac{2x^2-x}{x+2}\cdot\dfrac{2}{2x-1}=\dfrac{2x}{x+2}\)
b: Khi 4x2-1=0 thì (2x-1)(2x+1)=0
=>x=1/2(loại) và x=-1/2(nhận)
Khi x=-1/2 thì \(P=\left(2\cdot\dfrac{-1}{2}\right):\left(-\dfrac{1}{2}+2\right)=-1:\dfrac{3}{2}=-\dfrac{2}{3}\)
Với `x \ne +-2,x \ne 1/2,x \ne0`. Ta có:
`(3/[2x+4]+x/[2-x]+[2x^2+3]/[x^2-4]):[2x-1]/[4x-8]`
`=(3/[2(x+2)]-x/[x-2]+[2x^2+3]/[(x-2)(x+2)]).[4(x-2)]/[2x-1]`
`=[3(x-2)-2x(x+2)+2(2x^2+3)]/[x(x-2)(x+2)].[4(x-2)]/[2x-1]`
`=[3x-6-2x^2-4x+4x^2+6]/[x(x+2)]. 4/[2x-1]`
`=[2x^2-x]/[x(x+2)]. 4/[2x-1]`
`=[x(2x-1)]/[x(x+2)] . 4/[2x-1]`
`=4/[x+2]`
tham khảo:
\(P=\)\(\dfrac{8}{x^2+4x}\)+\(\dfrac{5}{x+4}\) - \(\dfrac{2}{x}\)
\(=\) \(\dfrac{8}{x\left(x+4\right)}\)+\(\dfrac{5x}{x\left(x+4\right)}\) - \(\dfrac{2\left(x+4\right)}{x\left(x+4\right)}\)
\(=\) \(\dfrac{8+5x-2x-8}{x\left(x+4\right)}\)
\(=\) \(\dfrac{3}{x\left(x+4\right)}\)
\(=\) \(\dfrac{3}{x+4}\)
Khi \(x =\) \(\dfrac{1}{2}\) thì \(P=\) \(\dfrac{3}{\dfrac{1}{2}+4}\) \(=\) \(\dfrac{2}{3}\)