tìm x biết
x(x+1) (x+6)-x^3=5x
Giúp mk đi
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\(\dfrac{x}{3}-\dfrac{1}{y+1}=\dfrac{1}{6}\)
=>\(\dfrac{xy+x-3}{3\left(y+1\right)}=\dfrac{1}{6}\)
=>\(2\left(xy+x-3\right)=1\)
=>2xy+2x-6=1
=>2xy+2x=7
=>2x(y+1)=7
=>x(y+1)=7/2
mà x,y nguyên
nên \(\left(x,y\right)\in\varnothing\)
1/y+1=x/3-1/6
1/y+1=2x/6-1/6
1/y+1= 2x-1/6
=> 1.6=(y+1).(2x-1)
ta có bảng
y+1 6 1
Past lives couldn't ever hold me down2x-1 1 6 ...
y 5 0
x 1 7/2
loại
\(\left(x-3\right)=\left(3-x\right)^2\)
\(\Leftrightarrow x-3=\left(x-3\right)^2\)
\(\Leftrightarrow\left(x-3\right)-\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(x-3\right)\left[1-\left(x-3\right)\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(4-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\4-x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
___________
\(x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}=\dfrac{1}{64}\)
\(\Leftrightarrow x^3+3\cdot\dfrac{1}{2}\cdot x^2+3\cdot\left(\dfrac{1}{2}\right)^2\cdot x+\left(\dfrac{1}{2}\right)^3=\dfrac{1}{64}\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^3=\left(\dfrac{1}{4}\right)^3\)
\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{1}{4}\)
\(\Leftrightarrow x=\dfrac{1}{4}-\dfrac{1}{2}\)
\(\Leftrightarrow x=-\dfrac{1}{4}\)
\(x=\dfrac{7}{25}+\dfrac{-1}{5}=\dfrac{7}{25}-\dfrac{1}{5}=\dfrac{2}{25}.\\ x=\dfrac{5}{11}+\dfrac{4}{-9}=\dfrac{5}{11}-\dfrac{4}{9}=\dfrac{1}{99}.\\ \dfrac{5}{9}-\dfrac{x}{-1}=\dfrac{-1}{3}\Leftrightarrow\dfrac{5}{9}+x=-\dfrac{1}{3}.\Leftrightarrow x=-\dfrac{8}{9}.\)
\(x=\dfrac{7}{25}+-\dfrac{1}{5}=>\dfrac{7}{25}+-\dfrac{5}{25}=>x=\dfrac{2}{25}\)
\(x=\dfrac{5}{11}+\dfrac{4}{-9}=>\dfrac{-45}{-99}+\dfrac{44}{-99}=>x=\dfrac{-1}{-99}=\dfrac{1}{99}\)
\(\dfrac{5}{9}-\dfrac{x}{-1}=-\dfrac{1}{3}=>-\dfrac{1}{3}-\dfrac{5}{9}=>\dfrac{x}{-1}=-\dfrac{8}{9}=>x=-\dfrac{8}{9}\)
1) \(\Rightarrow x^2\left(x^{2004}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{2004}=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
2) \(\Rightarrow\left(x-5\right)^4\left[\left(x-5\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^2=1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\\x-5=-1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\)
Bài 2:
a: =>x-45=-20
hay x=25
b: =>35+30-5x=-12+112
=>65-5x=100
=>5x=-35
hay x=-7
c: =>x-124=1000
hay x=1124
d: \(\Leftrightarrow46-\left(3x-2\right)^3=-18\)
\(\Leftrightarrow\left(3x-2\right)^3=64\)
=>3x-2=4
hay x=2
x(x+1) (x+6)-x3=5x
<=> ( x2 + x ) . ( x + 6 ) - x3 - 5x = 0
<=> x3 +6x2 +x2 + 6x - x3 -5x = 0
<=> 7x2 + x = 0
<=> x ( 7x + 1 ) = 0
<=> \(\orbr{\begin{cases}x=0\\7x+1=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=0\\x=-\frac{1}{7}\end{cases}}\)
Vay : phương trình có 2 nghiệm \(x_1=0;x_2=-\frac{1}{7}\)
CHÚC BẠN HỌC TỐT !!!
\(x\left(x+1\right)\left(x+6\right)-x^3=5x\)
\(< =>x^3+7x^2+6x-x^3-5x=0\)
\(< =>7x^2+x=0\)
\(< =>x\left(7x+1\right)=0\)
\(< =>\orbr{\begin{cases}x=0\\7x+1=0\end{cases}}\)
\(< =>\orbr{\begin{cases}x=0\\x=-\frac{1}{7}\end{cases}}\)