PT
1
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Các câu hỏi dưới đây có thể giống với câu hỏi trên
10 tháng 7 2018
a. \(2.\left(5x-8\right)-3.\left(4x-5\right)=4.\left(3x-4\right)+11\Leftrightarrow10x-16-12x+15=12x-16+11\\ \)
\(\Leftrightarrow-2x-1=12x-5\Leftrightarrow14x-4=0\Leftrightarrow x=\frac{2}{7}\)
AM
10 tháng 7 2018
\(a,2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\)
\(\Leftrightarrow10x-16-12x+15=12x-16+11\)
\(\Leftrightarrow10x-12x-12x=-16+11+16-15\)
\(\Leftrightarrow-14x=-4\)
\(\Leftrightarrow x=\frac{-4}{-14}=\frac{2}{7}\)
TH
Trần Hoàng Trung
VIP
29 tháng 8
a) \(\left(\right. x + y \left.\right)^{3} - \left(\right. x + y \left.\right) \left(\right. x^{2} - x y + y^{2} \left.\right) = 3 x y \left(\right. x + y \left.\right)\)
Giải:
Bắt đầu với vế trái của phương trình:
\(\left(\right. x + y \left.\right)^{3} - \left(\right. x + y \left.\right) \left(\right. x^{2} - x y + y^{2} \left.\right)\)
Bước 1: Mở rộng \(\left(\right. x + y \left.\right)^{3}\):
\(\left(\right. x + y \left.\right)^{3} = x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}\)
Bước 2: Mở rộng \(\left(\right. x + y \left.\right) \left(\right. x^{2} - x y + y^{2} \left.\right)\):
\(\left(\right. x + y \left.\right) \left(\right. x^{2} - x y + y^{2} \left.\right) = x \left(\right. x^{2} - x y + y^{2} \left.\right) + y \left(\right. x^{2} - x y + y^{2} \left.\right)\)\(= x^{3} - x^{2} y + x y^{2} + y x^{2} - x y^{2} + y^{3}\)\(= x^{3} + y^{3} + \left(\right. y x^{2} - x^{2} y \left.\right) = x^{3} + y^{3}\)
Bước 3: Trừ các biểu thức:
\(\left(\right. x + y \left.\right)^{3} - \left(\right. x + y \left.\right) \left(\right. x^{2} - x y + y^{2} \left.\right) = \left(\right. x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} \left.\right) - \left(\right. x^{3} + y^{3} \left.\right)\)\(= 3 x^{2} y + 3 x y^{2}\)\(= 3 x y \left(\right. x + y \left.\right)\)
Vậy, phương trình đã đúng:
\(\left(\right. x + y \left.\right)^{3} - \left(\right. x + y \left.\right) \left(\right. x^{2} - x y + y^{2} \left.\right) = 3 x y \left(\right. x + y \left.\right)\)
b) \(B = \left(\right. 3 x + 2 \left.\right) \left(\right. 9 x^{2} - 6 x + 4 \left.\right) - 3 \left(\right. 9 x^{3} - 2 \left.\right)\)
Giải:
Bước 1: Mở rộng \(\left(\right. 3 x + 2 \left.\right) \left(\right. 9 x^{2} - 6 x + 4 \left.\right)\):
\(\left(\right. 3 x + 2 \left.\right) \left(\right. 9 x^{2} - 6 x + 4 \left.\right) = 3 x \left(\right. 9 x^{2} - 6 x + 4 \left.\right) + 2 \left(\right. 9 x^{2} - 6 x + 4 \left.\right)\)\(= 27 x^{3} - 18 x^{2} + 12 x + 18 x^{2} - 12 x + 8\)\(= 27 x^{3} + 8\)
Bước 2: Mở rộng \(3 \left(\right. 9 x^{3} - 2 \left.\right)\):
\(3 \left(\right. 9 x^{3} - 2 \left.\right) = 27 x^{3} - 6\)
Bước 3: Trừ hai biểu thức:
\(B = \left(\right. 27 x^{3} + 8 \left.\right) - \left(\right. 27 x^{3} - 6 \left.\right) = 8 + 6 = 14\)
Vậy, \(B = 14\).
c) \(C = \left(\right. x - 2 \left.\right) \left(\right. x^{2} - 2 x + 4 \left.\right) - \left(\right. x^{3} - 7 \left.\right)\)
Giải:
Bước 1: Mở rộng \(\left(\right. x - 2 \left.\right) \left(\right. x^{2} - 2 x + 4 \left.\right)\):
\(\left(\right. x - 2 \left.\right) \left(\right. x^{2} - 2 x + 4 \left.\right) = x \left(\right. x^{2} - 2 x + 4 \left.\right) - 2 \left(\right. x^{2} - 2 x + 4 \left.\right)\)\(= x^{3} - 2 x^{2} + 4 x - 2 x^{2} + 4 x - 8\)\(= x^{3} - 4 x^{2} + 8 x - 8\)
Bước 2: Trừ biểu thức \(x^{3} - 7\):
\(C = \left(\right. x^{3} - 4 x^{2} + 8 x - 8 \left.\right) - \left(\right. x^{3} - 7 \left.\right)\)\(C = x^{3} - 4 x^{2} + 8 x - 8 - x^{3} + 7\)\(C = - 4 x^{2} + 8 x - 1\)
Vậy, \(C = - 4 x^{2} + 8 x - 1\).
d) \(D = \left(\right. x + 1 \left.\right)^{3} - \left(\right. x - 1 \left.\right) \left(\right. x^{2} + x + 1 \left.\right) - 3 x \left(\right. x + 1 \left.\right)\)
Giải:
Bước 1: Mở rộng \(\left(\right. x + 1 \left.\right)^{3}\):
\(\left(\right. x + 1 \left.\right)^{3} = x^{3} + 3 x^{2} + 3 x + 1\)
Bước 2: Mở rộng \(\left(\right. x - 1 \left.\right) \left(\right. x^{2} + x + 1 \left.\right)\):
\(\left(\right. x - 1 \left.\right) \left(\right. x^{2} + x + 1 \left.\right) = x \left(\right. x^{2} + x + 1 \left.\right) - 1 \left(\right. x^{2} + x + 1 \left.\right)\)\(= x^{3} + x^{2} + x - x^{2} - x - 1\)\(= x^{3} - 1\)
Bước 3: Mở rộng \(3 x \left(\right. x + 1 \left.\right)\):
\(3 x \left(\right. x + 1 \left.\right) = 3 x^{2} + 3 x\)
Bước 4: Trừ các biểu thức:
\(D = \left(\right. x^{3} + 3 x^{2} + 3 x + 1 \left.\right) - \left(\right. x^{3} - 1 \left.\right) - \left(\right. 3 x^{2} + 3 x \left.\right)\)\(D = x^{3} + 3 x^{2} + 3 x + 1 - x^{3} + 1 - 3 x^{2} - 3 x\)\(D = 2\)
Vậy, \(D = 2\).
e) \(E = 3 \left(\right. x - 1 \left.\right) \left(\right. x^{2} + x + 1 \left.\right) + x \left(\right. x + 1 \left.\right) - x \left(\right. x^{2} + x + 1 \left.\right)\)
Giải:
Bước 1: Mở rộng \(3 \left(\right. x - 1 \left.\right) \left(\right. x^{2} + x + 1 \left.\right)\):
\(3 \left(\right. x - 1 \left.\right) \left(\right. x^{2} + x + 1 \left.\right) = 3 \left(\right. x \left(\right. x^{2} + x + 1 \left.\right) - \left(\right. x^{2} + x + 1 \left.\right) \left.\right)\)\(= 3 \left(\right. x^{3} + x^{2} + x - x^{2} - x - 1 \left.\right) = 3 \left(\right. x^{3} - 1 \left.\right)\)\(= 3 x^{3} - 3\)
Bước 2: Mở rộng \(x \left(\right. x + 1 \left.\right)\):
\(x \left(\right. x + 1 \left.\right) = x^{2} + x\)
Bước 3: Mở rộng \(x \left(\right. x^{2} + x + 1 \left.\right)\):
\(x \left(\right. x^{2} + x + 1 \left.\right) = x^{3} + x^{2} + x\)
Bước 4: Trừ các biểu thức:
\(E = \left(\right. 3 x^{3} - 3 \left.\right) + \left(\right. x^{2} + x \left.\right) - \left(\right. x^{3} + x^{2} + x \left.\right)\)\(E = 3 x^{3} - 3 + x^{2} + x - x^{3} - x^{2} - x\)\(E = 2 x^{3} - 3\)
Vậy, \(E = 2 x^{3} - 3\).
g) \(9 x \left(\right. x + 1 \left.\right)^{3} + \left(\right. x - 1 \left.\right)^{3} = 2 x^{3}\)
Giải:
Mở rộng biểu thức và kiểm tra tính đúng đắn:
\(9 x \left(\right. x + 1 \left.\right)^{3} = 9 x \left(\right. x^{3} + 3 x^{2} + 3 x + 1 \left.\right) = 9 x^{4} + 27 x^{3} + 27 x^{2} + 9 x\)\(\left(\right. x - 1 \left.\right)^{3} = x^{3} - 3 x^{2} + 3 x - 1\)
Cộng cả hai biểu thức:
\(9 x \left(\right. x + 1 \left.\right)^{3} + \left(\right. x - 1 \left.\right)^{3} = 9 x^{4} + 27 x^{3} + 27 x^{2} + 9 x + x^{3} - 3 x^{2} + 3 x - 1\)\(= 9 x^{4} + 28 x^{3} + 24 x^{2} + 12 x - 1\)
So với \(2 x^{3}\), ta thấy biểu thức không đúng. Có thể bài toán có lỗi. Nếu có sự nhầm lẫn, bạn có thể điều chỉnh lại nhé!
h) \(\left(\right. x + 3 \left.\right) \left(\right. x^{2} - 3 x + 9 \left.\right) = x \left(\right. x^{2} - 3 x + 9 \left.\right) = x \left(\right. x^{2} + 4 \left.\right) - 1\)
JK
10 tháng 10 2019
a, (3x - 5)(2x - 1) - (x + 2)(6x - 1) = 0
=> 6x^2 - 3x - 10x + 5 - (6x^2 - x + 12x - 2) = 0
=> 6x^2 - 13x + 5 - 6x^2 - 11x + 2 = 0
=> -24x + 7 = 0
=> - 24x = -7
=> x = 7/24
b, (3x - 2)(3x + 2) - (3x - 1)^2 = -5
=> 9x^2 - 4 - 9x^2 + 6x - 1 = -5
=> 6x - 5 = -5
=> 6x = 0
=> x = 0
c, x^2 = -6x - 8
=> x^2 + 6x + 8 = 0
=> x^2 + 2.x.3 + 9 - 1 = 0
=> (x + 3)^2 = 1
=> x + 3 = 1 hoặc x + 3 = -1
=> x = -2 hoặc x = -4
13 tháng 11 2018
a) \(x-1-\dfrac{x^2-4}{x+1}=\dfrac{\left(x-1\right)\left(x+1\right)-\left(x^2-4\right)}{x+1}=\dfrac{x^2-1-x^2+4}{x+1}=\dfrac{3}{x+1}\)
b) \(\dfrac{3x-1}{2\left(3x+1\right)}+\dfrac{3x+1}{2\left(3x-1\right)}-\dfrac{6x}{\left(3x-1\right)\left(3x+1\right)}\)
\(=\dfrac{\left(3x-1\right)^2+\left(3x+1\right)^2-12x}{2\left(3x-1\right)\left(3x+1\right)}\)
\(=\dfrac{9x^2-6x+1+9x^2+6x+1-12x}{2\left(3x-1\right)\left(3x+1\right)}\)
\(=\dfrac{18x^2-12x+2}{2\left(3x-1\right)\left(3x+1\right)}\)
\(=\dfrac{9x^2-6x+1}{\left(3x-1\right)\left(3x+1\right)}\)
\(=\dfrac{\left(3x-1\right)^2}{\left(3x-1\right)\left(3x+1\right)}=\dfrac{3x-1}{3x+1}\)
20 tháng 11 2022
c: \(=\dfrac{1}{x-2}-\dfrac{x+4}{\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x\left(x+2\right)}\)
\(=\dfrac{x\left(x+2\right)-x^2-4x-2x+4}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+2x-x^2-6x+4}{x\left(x-2\right)\left(x+2\right)}=\dfrac{-4x+4}{x\left(x-2\right)\left(x+2\right)}\)
d: Sửa đề: \(\dfrac{2x^2+1}{x^3+1}-\dfrac{x-1}{x^2-x+1}-\dfrac{1}{x+1}\)
\(=\dfrac{2x^2+1-x^2+1-x^2+x-1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{1}{x^2-x+1}\)
KH
10 tháng 12 2018
1.
a) \(x\left(x+4\right)+x+4=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
b) \(x\left(x-3\right)+2x-6=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)
10 tháng 12 2018
Bài 1:
a, \(x\left(x+4\right)+x+4=0\)
\(\Leftrightarrow x\left(x+4\right)+\left(x+4\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
Vậy \(x=-4\) hoặc \(x=-1\)
b, \(x\left(x-3\right)+2x-6=0\)
\(\Leftrightarrow x\left(x-3\right)+2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Vậy \(x=3\) hoặc \(x=-2\)
10 tháng 10 2019
a) \(\left(3x-5\right)\left(2x-1\right)-\left(x+2\right)\left(6x-1\right)=0\)
⇔ \(6x^2-13x+5-6x^2-11x+2=0\)
⇔ \(24x=7\)⇔\(x=\frac{7}{24}\)
b) \(\left(3x-2\right)\left(3x+2\right)-\left(3x-1\right)^2=-5\)
⇔ \(9x^2-4-9x^2+6x-1=5\)
⇔ \(6x=10\)⇔ \(x=\frac{5}{3}\)
c) \(x^2=-6x-8\)⇔\(x^2+6x+8=0\)⇔\(\left(x+2\right)\left(x+4\right)=0\)
⇔\(\left[{}\begin{matrix}x=-2\\x=-4\end{matrix}\right.\)
Ta có