Thực hiện phép tính:
a) ( x + 3 ) 3 ; b) x − 2 5 3 ;
c) 3 m 2 + n 4 3 ; d) − 2 3 u 3 − 3 2 v 2 3 .
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\(a,=\left(x^3+3x^2-x^2-3x+x+3\right):\left(x+3\right)\\ =\left(x+3\right)\left(x^2-x+1\right):\left(x+3\right)\\ =x^2-x+1\\ b,=\left(x^3+2x^2-x^2-2x+3x+6\right):\left(x+2\right)\\ =\left(x+2\right)\left(x^2-x+3\right):\left(x+2\right)\\ =x^2-x+3\)
\(\left(\dfrac{1}{x}+x-2\right):\left(\dfrac{1}{x^2-x}+1-\dfrac{3}{x-1}\right)\)
\(=\dfrac{x^2-2x+1}{x}:\dfrac{1+x^2-x-3x}{x\left(x-1\right)}\)
\(=\dfrac{\left(x-1\right)^2}{x}\cdot\dfrac{x\left(x-1\right)}{x^2-4x+1}=\dfrac{\left(x-1\right)^3}{x^2-4x+1}\)
a:\(2x^2y\left(3x^2-5xy+4y^2\right)-6x^4y-10x^3y^2+8x^2y^3\)
b: \(\left(x^2-9\right)^2-\left(x+3\right)\left(x-3\right)\left(x^2+9\right)\)
\(=x^4-18x^2+81-\left(x^4-81\right)\)
\(=-18x^2+162\)
a) = x^2 - 9 - (x^2 + 3x - 10)
= -3x + 1
b) = 3x + 1 - 3x + 19
= 20
a: \(\left(x+3\right)\left(x-3\right)-\left(x-2\right)\left(x+5\right)\)
\(=x^2-9-x^2-3x+10\)
\(=-3x+1\)
b: \(\dfrac{27x^3+1}{9x^2-3x+1}-\left(3x-19\right)\)
\(=3x+1-3x+19\)
=20
a) \(2xy\left(3x^2-5xy+4y^2\right)=6x^3y-10x^2y^2+8xy^3\)
b) \(\left(x-3\right)^2+\left(x+5\right)\left(5-x\right)=x^2-6x+9+25-x^2=34-6x\)
a: \(2xy\left(3x^2-5xy+4y^2\right)=6x^3y-10x^2y^2+8xy^3\)
b: \(\left(x-3\right)^2+\left(x+5\right)\left(5-x\right)\)
\(=x^2-6x+9+25-x^2\)
=-6x+34
a: =>x>=0 và x^2+x=x^2
=>x=0
b: =>x>=2 và x^2-4x-3=x^2-4x+4
=>-3=4(loại)
\(a)ĐK:x\ge0\)
\(pt\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x^2+x=x^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x=0\left(tm\right)\end{matrix}\right.\)
Vậy, pt có nghiệm duy nhất là x=0
\(b)ĐK:x\ge2+\sqrt{7}\)
\(pt\Leftrightarrow\left\{{}\begin{matrix}x-2\ge0\\x^2-4x-3=(x-2)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x^2-4x-3=x^2-4x+4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\-3=4\end{matrix}\right.\)(vô lý)
Vậy pt vô nghiệm
Tham khảo
a)
-7x2(3x - 4y)
= -7x2.3x + 7x2ư.4y
= -21x2 + 28x2y
b)
(x - 3)(5x - 4)
= x.5x - x.4 - 3.5x + 3.4
= 5x2 - 4x - 15x + 12
= 5x2 - 19x + 12
c)
(2x - 1)2 = 4x2 - 4x + 1
d)
(x + 3)(x - 3) = x2 - 32 = x2 - 9
a) \(\left(5x-4y^3\right)\left(2x^2-1+y\right)=10x^3-5x+5xy-8x^2y^3+4y^3-4y^4=-4y^4+10x^3+4y^3-8x^2y^3+5xy-5x\)
b) \(\left(x-3\right)\left(2x-1\right)-\left(2x-7\right)x=2x^2-7x+3-2x^2+7x=3\)
a) (x-2)(x+2)-x(x-1)+8
= x2-4-x2+x+8
= (x2-x2)+(-4+8)+x
= 4+x
b) bn viết lại đề đi:v
đọc khó quá.
a)\(\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4=x^4-y^4\)
b) \(x\left(3x-18\right)-3\left(x-4\right)\left(x-2\right)+8=3x^2-18x-3x^2+18x-24+8=-16\)
a) x 3 + 9 x 2 + 27x + 27.
b) x 3 − 6 5 x 2 + 12 25 x − 8 125 .
c) 27 m 6 + 27 4 m 4 n + 9 16 m 2 n 2 + n 3 64 .
d) − 8 27 u 9 − 2 u 6 v 2 − 9 2 u 3 v 4 − 27 8 v 6 .