Làm tính chia:
a/ \(\left(x^4-x^3+x^2+3x\right):\left(x^2-2x+3\right)\)
b/ \(\left(x^2-y^2+6x+9\right):\left(x+y+3\right)\)
Làm tính chia :
a) \(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\)
b) \(\left(x^4-x^3+x^2+3x\right):\left(x^2-2x+3\right)\)
c) \(\left(x^2-y^2+6x+9\right):\left(x+y+3\right)\)
a) \(\left( {6{x^3} - 7{x^2} - x + 2} \right):\left( {2x + 1} \right)\)
b) $(x^4-x^3+x^2+3x):(x^2-2x+3)$
c) \(\left( {{x^2} + {y^2} + 6x + 9} \right):\left( {x + y + 3} \right)\)
\(=\left( {{x^2} + 6x + 9 - {y^2}} \right)\left( {x + y + 3} \right)\)
\(=\left[ {\left( {{x^2} + 2x.3 + {3^2}} \right) - {y^2}} \right]:\left( {x + y + 3} \right)\)
\(=\left[ {{{\left( {x + 3} \right)}^2} - {y^2}} \right]:\left( {x + y + 3} \right)\)
\(=\left( {x + 3 - y} \right)\left( {x + 3 + y} \right):\left( {x + y + 3} \right)\)
$= x + 3 - y$
$= x - y + 3$
(6x3 - 7x2 - x + 2) : (2x + 1)
= (6x3 + 3x2 - 10x2 - 5x + 4x + 2) : (2x + 1)
= [(6x3 + 3x2) - (10x2 + 5x) + (4x + 2)] : (2x + 1)
= [3x2(2x + 1) - 5x(2x + 1) + 2(2x + 1)] : (2x + 1)
= (3x2 - 5x + 2)(2x + 1) : (2x + 1)
= 3x2 - 5x + 2
(x4 - x3 + x2 + 3x) : (x2 - 2x + 3)
= (x4 + x3 - 2x3 - 2x2 + 3x2 + 3x) : (x2 - 2x + 3)
= [(x4 + x3) - (2x3 + 2x2) + (3x2 + 3x)] : (x2 - 2x + 3)
= [x3(x + 1) - 2x2(x + 1) + 3x(x + 1)] : (x2 - 2x + 3)
= (x3 - 2x2 + 3x)(x + 1) : (x2 - 2x + 3)
= x(x2 - 2x + 3)(x + 1): (x2 - 2x + 3)
= x(x + 1)
= x2 + x
(x2 - y2 + 6x + 9) : (x + y + 3)
= [(x2 + 6x + 9) - y2] : (x + y + 3)
= [(x + 3)2 - y2] : (x + y + 3)
= (x + 3 + y)(x + 3 - y) : (x + y + 3)
= (x + y + 3)(x - y + 3) : (x + y + 3)
= x - y + 3
CHÚC BN HOK TỐT
c) (x2+y2+6x+9):(x+y+3)
= (x2+6x+9−y2)(x+y+3)
= [(x2+2x.3+32)−y2]:(x+y+3)
= [(x+3)2−y2]:(x+y+3)
= (x+3−y)(x+3+y):(x+y+3)
= x + 3 - y
= x - y + 3
a) làm tính chia
\(\left[5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2\right]:\left(y-x\right)^2\)
b) tìm \(x\)
\(\left(4x^4-3x^3\right):\left(-x^3\right)+\left(15x^2+6x\right):3x=0\)
ghi chú: đừng làm tắt được ko ạ?
b: Ta có: \(\left(4x^4-3x^3\right):\left(-x^3\right)+\left(15x^2+6x\right):3x=0\)
\(\Leftrightarrow-4x+3+5x+2=0\)
\(\Leftrightarrow x=-5\)
Làm tính chia:
a) \(5^3:\left(-5\right)^2\)
b) \(\left(\dfrac{3}{4}\right)^5:\left(\dfrac{3}{4}\right)^3\)
c) \(\left(-12\right)^3-8^3\)
d) \(x^{10}:\left(-x\right)^8\)
e) \(\left(-x\right)^5:\left(-x\right)^3\)
f) \(\left(-y\right)^5:\left(-y\right)^4.\)
\(a,=5^3:5^2=5\\ b,=\left(\dfrac{3}{4}\right)^{5-3}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}\\ c,=1728-512=1216\\ d,=x^{10}:x^8=x^2\\ e,=\left(-x\right)^{5-3}=\left(-x\right)^2=x^2\\ f,=\left(-y\right)^{5-4}=-y\)
Tính đạo hàm:
a) y= \(\left(x^5+2x\right).\left(x^6-3\right).\left(3x^7+6x^2-2\right)\)
b) y= \(\left(x^4-\dfrac{2}{3x}\right)^5\)tại x=10
c) y= \(\dfrac{5x-2}{x+1}\) tại x=4
a. Làm gọn 1 chút xíu:
\(y=\left(x^{11}+2x^7-3x^5-6x\right)\left(3x^7+6x^2-2\right)\)
\(y'=\left(11x^{10}+14x^6-15x^4-6\right)\left(3x^7+6x^2-2\right)+\left(21x^6+12x\right)\left(x^{11}+2x^7-3x^5-6x\right)\)
b.
\(y'=5\left(x^4-\dfrac{2}{3x}\right)^4\left(4x^3+\dfrac{2}{3x^2}\right)\Rightarrow y'\left(10\right)=5\left(10^4-\dfrac{2}{30}\right)^4\left(4.10^3+\dfrac{2}{300}\right)=?\)
c.
\(y'=\dfrac{7}{\left(x+1\right)^2}\Rightarrow y'\left(4\right)=\dfrac{7}{25}\)
Thực hiện các phép chia:
a) \(\left( {4{x^3}{y^2} - 8{x^2}y + 10xy} \right):\left( {2xy} \right)\) b) \(\left( {7{x^4}{y^2} - 2{x^2}{y^2} - 5{x^3}{y^4}} \right):\left( {3{x^2}y} \right)\)
`a, (4x^3y^2 - 8x^2y + 10xy) : 2xy`
`= 2x^2y - 4x + 5`.
`b, 7x^4y^2 - 2x^2y^2 - 5x^3y^4 : 3x^2y`
`= 7/3 x^2y - 3/2y - 5/3xy^3`
Rút gọn:
a) \(\dfrac{3\left(x-y\right)\left(x-z\right)^2}{6\left(x-y\right)\left(x-z\right)}\)
b) \(\dfrac{6x^2y^2}{8xy^5}\)
c) \(\dfrac{3x\left(1-x\right)}{2\left(x-1\right)}\)
d) \(\dfrac{9-\left(x+5\right)^2}{x^2+4x+4}\)
e) \(\dfrac{x^2-2x+1}{x^2-1}\)
f) \(\dfrac{8x-4}{8x^3-1}\)
g) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)
k) \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)
a: \(=\dfrac{x-z}{2}\)
b: \(=\dfrac{3x}{4y^3}\)
Tính:
\(a)\left(-2x^2\right)\cdot\left(3x-4x^3+7-x^2\right)\)
\(b)\left(x+3\right)\cdot\left(2x^2-3x-5\right)\)
\(c)\left(-6x^5+7x^4-6x^3\right):3x^3\)
\(d)\left(9x^2-4\right):\left(3x+2\right)\)
\(e)\left(2x^4-13x^3+15x^2+11x-3\right):\left(x^2-4x-3\right)\)
a: \(=-2x^2\cdot3x+2x^2\cdot4X^3-2x^2\cdot7+2x^2\cdot x^2\)
\(=8x^5+2x^4-6x^3-14x^2\)
b: \(=2x^3-3x^2-5x+6x^2-9x-15\)
\(=2x^3+3x^2-14x-15\)
c: \(=\dfrac{-6x^5}{3x^3}+\dfrac{7x^4}{3x^3}-\dfrac{6x^3}{3x^3}=-2x^2+\dfrac{7}{3}x-2\)
d: \(=\dfrac{\left(3x-2\right)\left(3x+2\right)}{3x+2}=3x-2\)
e: \(=\dfrac{2x^4-8x^3-6x^2-5x^3+20x^2+15x+x^2-4x-3}{x^2-4x-3}\)
=2x^2-5x+1
1)rút gọn
a) (x+5)(\(x^2\) - 5x + 25) - \(\left(x+3\right)^3\) + (x-2)(\(x^2\) + 2x + 4) - \(\left(x-1\right)^3\)
b)\(\left(x+3y\right)^3+\left(3x+2y\right)\left(9x^2-6xy+4y^2\right)-\left(2y-3x\right)^3\)
c)\(\left(3x+y\right)^3-\left(5x-y\right)\left(25x^2+5xy+y^2\right)+\left(x+2y\right)^3\)
2)tìm x,biết
a)\(\left(x-1\right)^2-\left(x-2\right)\left(x+3\right)+\left(x+2\right)^3=\left(x-3\right)\left(x^2+3x+9\right)+6x\left(x+2\right)\)
Cảm ơn các bạn ^^
\(\left(x^2-x^3\right).\left(x-5\right)\)
\(\left(x+3\right)\left(x^2-3x+9\right)\)
\(\left(2x+y^2\right).\left(2x-y^2\right)\)
\(\left(x+3\right)\left(x^2-3x+9\right)=x^3+27\)
\(\left(2x+y^2\right)\left(2x-y^2\right)=4x^2-y^4\)