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\(\frac{1}{\left(x-1\right)x}+\frac{1}{\left(x-2\right)\left(x-1\right)}+\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-4\right)\left(x-3\right)}=\frac{x}{x^2-4x}\)
\(\Leftrightarrow\)\(\frac{1}{x-1}-\frac{1}{x}+\frac{1}{x-2}-\frac{1}{x-1}+\frac{1}{x-3}-\frac{1}{x-2}+\frac{1}{x-4}-\frac{1}{x-3}=\frac{x}{x\left(x-4\right)}\)
\(\Leftrightarrow\)\(-\frac{1}{x}+\frac{1}{x-4}=\frac{1}{x-4}\)
\(\Leftrightarrow\)\(\frac{-\left(x-4\right)+x}{x\left(x-4\right)}=\frac{x}{x\left(x-4\right)}\)
\(\Leftrightarrow\)\(4-x+x=x\)
\(\Leftrightarrow x=4\)
lo nói mk làm cách lâu chứ m cx hỏi người khác!!!!!!!!!!!
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a/ \(x=\dfrac{-5}{12}\)
b/ \(x\approx-1,9526\)
c/ \(x=\dfrac{21-i\sqrt{199}}{10}\)
d/ \(x=\dfrac{-20}{13}\)
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6(x + 1)2 - 2(x + 1)3 + 2(x - 1)(x2 + x + 1) = 0
<=> 6(x2 + 2x + 1) - 2(x3 + 3x2 + 3x + 1) + 2(x - 1)(x2 + x + 1) = 0
<=> 6.x2 + 6.2x + 6.1 + (-2).x3 + (-2).3x2 + (-2).3x + (-2).1 + 2.x3 + 2(-1) = 0
<=> 6x2 + 12x + 6 - 2x3 - 6x2 - 6x - 2 + 2x3 - 2 = 0
<=> (6x2 - 6x2) + (12x - 6x) + (6 - 2 - 2) + (-2x3 + 2x2) = 0
<=> 6x + 2 = 0
<=> 6x = 0 - 2
<=> 6x = -2
<=> x = -2/6 = -1/3
=> x = -1/3
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(x+1) * (x2 +x+1) * (x-1) * (x2-x+1) = 7
[(x+1) * (x2 +x+1) ]*[(x-1) * (x2-x+1)]= 7 [Áp dụng hằng đẳng thức a3+b3=(a+b)*(a2+ab+b2)]
(x3+13) * (x3-13) = 7
x3 * x3 - x3 * 13 + x3 * 13 - 13 *13 =7
(x3)2 - 1 = 7
(x3)2 =7+1
(x3)2 =8
suy ra x = 3 căn 2
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Đặt \(t=\left(x+\frac{1}{x}\right)^2\)\(\Rightarrow\)\(x^2+\frac{1}{x^2}=t-2\)điều kiện t>=0,x # 0
Phương trình trở thành
8t +4(t-2)2 - 4(t-2)2t =(x+4)2
8t + 4t2 - 16t + 16 -4t3 + 16t2 - 16t=(x+4)2
-4t3 + 20t2 -24t=x2 +8x
-4t(t2 -5t +6)=x(x+8)
-4t(t-2)(t-3)=x(x+8)
Mình chỉ giúp dược tới đó
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\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+\right)\left(x+3\right)}+...+\frac{1}{\left(x+2015\right)\left(x+2016\right)}=\frac{1}{x+2016}\)
\(\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}+...+\frac{1}{x+2015}-\frac{1}{x+2016}=\frac{1}{x+2016}\)
\(\frac{1}{x}-\frac{1}{x+2016}=\frac{1}{x+2016}\)
\(\frac{1}{x}-\frac{1}{x+2016}-\frac{1}{x+2016}=0\)
\(\frac{1}{x}-\frac{2x}{x+2016}=0\)
\(\frac{x+2016}{x\left(x+2016\right)}-\frac{2x}{x\left(x+2016\right)}=0\)
\(\frac{x+2016-2x}{x\left(x+2016\right)}=0\Leftrightarrow2016-x=0\Leftrightarrow x=2016\)
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1: Ta có: \(4x^2-36=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
2: Ta có: \(\left(x-1\right)^2+x\left(4-x\right)=11\)
\(\Leftrightarrow x^2-2x+1+4x-x^2=11\)
\(\Leftrightarrow2x=10\)
hay x=5
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(x-1)^3-(x+3)(x^2-3x+9)+3(x^2-4)=2
=>x^3-3x^2+3x-1-x^3-27+3x^2-12=2
=>3x-40=2
=>x=42/3=14
=>cụm x+1sẽ bằng 1 hoặc 0
+,Nếu x+1=0
vậy x = -1
+,Nếu x+1 =2
vậy x=1
vậy x thuộc{-1;1}
\(x+1=\left(x+1\right)^2\)
\(\Leftrightarrow\)\(\left(x+1\right)^2+\left(x+1\right)=0\)
\(\Leftrightarrow\)\(\left(x+1\right)\left(x+1+1\right)=0\)
\(\Leftrightarrow\)\(\left(x+1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x+1=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-2\end{cases}}}\)
Vậy \(x=-1\) hoặc \(x=-2\)
Chúc bạn học tốt ~