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17 tháng 4 2021
\(\dfrac{8-2x}{x^2+x-20}=-\dfrac{2\left(4-x\right)}{\left(4-x\right)\left(x+5\right)}=\dfrac{-2}{x+5}\)
Để biểu thức trên nhận giá trị dương khi
\(x+5< 0\)do -2 < 0
\(\Leftrightarrow x< -5\)
11 tháng 12 2023
d: \(D=x^3-6x^2+12x-100\)
\(=x^3-6x^2+12x-8-92\)
\(=\left(x-2\right)^3-92\)
Khi x=-98 thì \(D=\left(-98-2\right)^3-92=-1000000-92=-1000092\)
e: \(E=\left(x+1\right)^3+6\left(x+1\right)^2+12x+20\)
\(=\left(x+1\right)^3+6\left(x+1\right)^2+12\left(x+1\right)+8\)
\(=\left(x+1+2\right)^3\)
\(=\left(x+3\right)^3\)
Khi x=5 thì \(E=\left(5+3\right)^3=8^3=512\)
f: \(F=\left(2x-1\right)\left(4x^2+2x+1\right)-7\left(x^3+1\right)\)
\(=\left(2x\right)^3-1^3-7x^3-7\)
\(=x^3-8\)
Khi x=-1/2 thì \(F=\left(-\dfrac{1}{2}\right)^3-8=-\dfrac{1}{8}-8=-\dfrac{65}{8}\)
g: \(G=\left(-x-2\right)^3+\left(2x-4\right)\left(x^2+2x+4\right)-x^2\left(x-6\right)\)
\(=-\left(x+2\right)^3+2\left(x-2\right)\left(x^2+2x+4\right)-x^3+6x^2\)
\(=-x^3-6x^2-12x-8+2\left(x^3-8\right)-x^3+6x^2\)
\(=-2x^3-12x-8+2x^3-16=-12x-24\)
Khi x=-2 thì \(G=-12\cdot\left(-2\right)-24=24-24=0\)
h: \(H=\left(x-1\right)^3-\left(x+2\right)\left(x^2-2x+4\right)+3\left(x+4\right)\left(x-4\right)\)
\(=x^3-3x^2+3x-1-\left(x^3+8\right)+3\left(x^2-16\right)\)
\(=x^3-3x^2+3x-1-x^3-8+3x^2-48\)
\(=3x-57\)
Khi x=-1/2 thì \(H=3\cdot\dfrac{-1}{2}-57=-1,5-57=-58,5\)
19 tháng 8 2023
\(=\dfrac{3a^2-3ab+ab-b^2}{2a^2+2ab-ab-b^2}:\dfrac{3a^2-3ab-ab+b^2}{3a^2+3ab-ab-b^2}\)
\(=\dfrac{\left(a-b\right)\left(3a+b\right)}{\left(a+b\right)\left(2a-b\right)}\cdot\dfrac{\left(a+b\right)\left(3a-b\right)}{\left(a-b\right)\left(3a-b\right)}\)
\(=\dfrac{\left(3a+b\right)}{2a-b}\)
H9
HT.Phong (9A5)
CTVHS
19 tháng 8 2023
\(R=\dfrac{3a^2-2ab-b^2}{2a^2+ab-b^2}:\dfrac{3a^2-4ab+b^2}{3a^2+2ab-b^2}\)
\(R=\dfrac{3a^2-3ab+ab-b^2}{2a^2+2ab-ab-b^2}:\dfrac{3a^2-3ab-ab+b^2}{3a^2+3ab-ab-b^2}\)
\(R=\dfrac{\left(3a^2-3ab\right)+\left(ab-b^2\right)}{\left(2a^2+2ab\right)-\left(ab+b^2\right)}:\dfrac{\left(3a^2-3ab\right)-\left(ab-b^2\right)}{\left(3a^2+3ab\right)-\left(ab+b^2\right)}\)
\(R=\dfrac{3a\left(a-b\right)+b\left(a-b\right)}{2a\left(a+b\right)-b\left(a+b\right)}\cdot\dfrac{3a\left(a+b\right)-b\left(a+b\right)}{3a\left(a-b\right)-b\left(a-b\right)}\)
\(R=\dfrac{\left(a-b\right)\left(3a+b\right)}{\left(a+b\right)\left(2a-b\right)}\cdot\dfrac{\left(a+b\right)\left(3a-b\right)}{\left(a-b\right)\left(3a-b\right)}\)
\(R=\dfrac{\left(a-b\right)\left(3a+b\right)}{\left(a+b\right)\left(2a-b\right)}\cdot\dfrac{a+b}{a-b}\)
\(R=\dfrac{3a+b}{2a-b}\)
H
24 tháng 8 2023
ĐK: \(\left\{{}\begin{matrix}x\ne1\\x\ne0\\x\ne2\end{matrix}\right.\)
Khi đó:
\(B=\left(\dfrac{x}{x\left(x-1\right)}-\dfrac{x-1}{x\left(x-1\right)}\right):\left(\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}-\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}\right)\\ =\dfrac{1}{x\left(x-1\right)}:\left(\dfrac{x^2-1-x^2+4}{\left(x-2\right)\left(x-1\right)}\right)\\ =\dfrac{1}{x\left(x-1\right)}.\dfrac{\left(x-2\right)\left(x-1\right)}{3}\\ =\dfrac{x-2}{3x}\)
24 tháng 8 2023
\(B=\left(\dfrac{1}{x-1}-\dfrac{1}{x}\right):\left(\dfrac{x+1}{x-2}-\dfrac{x+2}{x-1}\right)\)
\(=\dfrac{x-x+1}{x\left(x-1\right)}:\dfrac{\left(x+1\right)\left(x-1\right)-\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}\)
\(=\dfrac{1}{x\left(x-1\right)}\cdot\dfrac{\left(x-2\right)\left(x-1\right)}{x^2-1-x^2+4}\)
\(=\dfrac{\left(x-2\right)}{3x}\)
PT
1
16 tháng 7 2023
`@` `\text {Ans}`
`\downarrow`
`a)`
\((x+3)^2 - (x-4)(x+4)\)
`= (x^2 + 6x + 9) - (x^2 + 4x - 4x - 16)`
`= x^2 + 6x + 9 - (x^2 - 16)`
`= x^2 + 6x + 9 - x^2 + 16`
`= 6x + 25`
`b)`
\(3(x+2)^2 + (2x-1)^2 - 7(3+x)(x-3)\)
`= 3(x^2 + 4x + 4) + (4x^2 - 4x + 1) - 7(x^2 - 9)`
`= 3x^2 + 12x + 12 + 4x^2 - 4x + 1 - 7x^2 + 63`
`= (3x^2 + 4x^2 - 7x^2) + (12x - 4x) + (12 + 1 + 63)`
`= 8x + 76`
`c)`
\((x+2)^2 + (x-3)^2 - 2(x+1)(x-1)\)
`= (x^2 + 4x + 4) + (x^2 - 6x + 9) - 2(x^2 - 1)`
`= x^2 + 4x + 4 + x^2 - 6x + 9 - 2x^2 + 2`
`= (x^2 + x^2 - 2x^2) + (4x - 6x) + (4 + 9 + 2)`
`= -2x + 15`
`d)`
\((x+1)^3 - x(x-2)^2 + x - 1\)
`= (x^3 + 3x^2 + 3x + 1) - x(x^2 - 4x + 4) + x - 1`
`= x^3 + 3x^2 + 3x + 1 - x^3 + 4x^2 - 4x + x - 1`
`= (x^3 - x^3) + (3x^2 + 4x^2) + (3x - 4x + x) + (1-1)`
`= 7x^2 `
`@` `\text {Kaizuu lv uuu}`
13 tháng 8 2023
1: =x^3-6x^2+12x-8+x^3+6x^2+12x-8
=2x^3+24x
2: =x^3-3x^2+3x-1-x^3-3x^2-3x-1
=-6x^2-2
3: =1-3x+3x^2-x^3+x^3+9x^2+27x+27
=24x+12x^2+28
4: =x^3+6x^2y+12xy^2+8y^3-x^3+6x^2y-12xy^2+8y^3
=12x^2y+16y^3
5: =y^3-3y^2x+3yx^2-x^3-8x^3+12x^2y-6xy^2+y^3
=2y^3-9xy^2+15x^2y-9x^3
7: =8x^3-36x^2+54x-27-2x(4x^2+4x+1)
=8x^3-36x^2+54x-27-8x^3-8x^2-2x
=-44x^2+52x-27
8: =27x^3-27x^2+9x-1-27x^3-27x^2
=-54x^2+9x-1
\(a,y\left(12y+3\right)+4\left(7-3y^2\right)=12y^2+3y+28-12y^2=3y+28\\ b,\left(x-2\right)^2-\left(3x+1\right)\left(x-3\right)=\left(x^2-4x+4\right)-\left(3x^2+x-9x-3\right)=x^2-4x+4-3x^2-x+9x+3=-2x^2+4x+7\)
a) y(12y + 3) + 4( 7- 3y2) = 12y2 + 3y + 28 - 12y2= 3y + 28
b)( x -2)2 - (3x + 1)(x - 3) = x2 - 4x +4 -(3x2 - 9x + x - 3)
=x2 - 4x +4 - 3x2 + 9x -x +3
= -2x2 + 4x +7