Tìm x:
C)x⋮3,x<20
D)16⋮x,0<x<16
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\(c,\Rightarrow\left(x-2\right)-\left(x-2\right)^2=0\\ \Rightarrow\left(x-2\right)\left(1-x+2\right)=0\\ \Rightarrow\left(x-2\right)\left(3-x\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\\ d,\Rightarrow\left(x^2+3\right)\left(x+1\right)+\left(x+1\right)=0\\ \Rightarrow\left(x^2+3+1\right)\left(x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2+4=0\left(vô.nghiệm\right)\\x+1=0\end{matrix}\right.\Rightarrow x=-1\)
c. \(2\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)-\dfrac{3}{2}=\dfrac{1}{4}\)
\(2\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{1}{4}+\dfrac{3}{2}=\dfrac{7}{4}\)
\(\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{7}{4}:2=\dfrac{7}{8}\)
\(\dfrac{1}{2}x=\dfrac{7}{8}+\dfrac{1}{3}=\dfrac{29}{24}\)
\(x=\dfrac{29}{24}:\dfrac{1}{2}=\dfrac{29}{12}\)
Vậy : ...
d. \(\dfrac{4}{5}-\dfrac{1}{2}x=\dfrac{1}{10}\)
\(-\dfrac{1}{2}x=\dfrac{1}{10}-\dfrac{4}{5}=-\dfrac{7}{10}\)
\(x=-\dfrac{7}{10}:\left(-\dfrac{1}{2}\right)=\dfrac{7}{5}\)
Vậy : ...
c) \(2\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)-\dfrac{3}{2}=\dfrac{1}{4}\)
\(\Rightarrow2\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{1}{4}+\dfrac{3}{2}\)
\(\Rightarrow2\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{1}{4}+\dfrac{6}{4}\)
\(\Rightarrow2\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{7}{4}\)
\(\Rightarrow\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{7}{4}:2\)
\(\Rightarrow\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{7}{4}.\dfrac{1}{2}\)
\(\Rightarrow\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)=\dfrac{7}{8}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{7}{8}+\dfrac{1}{3}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{21}{24}+\dfrac{8}{24}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{29}{24}\)
\(\Rightarrow x=\dfrac{29}{24}:\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{29}{24}.2\)
\(\Rightarrow x=\dfrac{29}{12}\)
d) \(\dfrac{4}{5}-\dfrac{1}{2}x=\dfrac{1}{10}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{4}{5}-\dfrac{1}{10}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{8}{10}-\dfrac{1}{10}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{7}{10}\)
\(\Rightarrow x=\dfrac{7}{10}:\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{7}{10}.2\)
\(\Rightarrow x=\dfrac{7}{5}\)
c) 140:(x-8)=14
x-8 =140:14
x-8 =10
x =10+8
x =18
vậy...
d) 11(x-9)=88
x-9 =88:11
x-9 =8
x =8+9
x =17
vậy...
\(c.\left(1-2x\right)^2-\left(3x-2\right)^2=0\)
\(\left(1-2x-3x+2\right)\left(1-2x+3x-2\right)=0\)
\(\left(-5x+3\right)\left(x-1\right)=0\)
\(\left[{}\begin{matrix}-5x+3=0\\-x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\\x=1\end{matrix}\right.\)
\(d.\left(x-2\right)^2-\left(5-2x\right)^2=0\)
\(\left(x-2-5+2x\right)\left(x-2+5-2x\right)=0\)
\(\left(3x-7\right)\left(-x+3\right)=0\)
\(\left[{}\begin{matrix}3x-7=0\\-x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=3\end{matrix}\right.\)
\(c,\Leftrightarrow1-4x+4x^2=9x^2-12x+4\\ \Leftrightarrow5x^2-8x+3=0\\ \Leftrightarrow\left(x-1\right)\left(5x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{3}{5}\end{matrix}\right.\\ d,\Leftrightarrow\left(x-2-5+2x\right)\left(x-2+5-2x\right)=0\\ \Leftrightarrow\left(3x-7\right)\left(3-x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=3\end{matrix}\right.\)
`c,(x-2)(2x-1)-(2x-3)(x-1)-2`
`=2x^2-x-4x+2-2x^2+2x+3x-3-2`
`=-3`
`->` Biểu thức không phụ thuộc vào biến `x`
\(C=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)-x^{64}\\ =\left(x^4-1\right)\left(x^4+1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)-x^{64}\\ =\left(x^8-1\right)\left(x^8+1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)-x^{64}\\ =\left(x^{16}-1\right)\left(x^{16}+1\right)\left(x^{32}+1\right)-x^{64}\\ =\left(x^{32}-1\right)\left(x^{32}+1\right)-x^{64}\\ =\left(x^{64}-1\right)-x^{64}\\ =-1\)
Vậy đa thức ko phụ thuộc vào x
\(C=(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^{16}+1)(x^{32}+1)-x^{64}\\=(x^4-1)(x^4+1)(x^8+1)(x^{16}+1)(x^{32}+1)-x^{64}\\=(x^8-1)(x^8+1)(x^{16}+1)(x^{32}+1)-x^{64}\\=(x^{16}-1)(x^{16}+1)(x^{32}+1)-x^{64}\\=(x^{32}-1)(x^{32}+1)-x^{64}\\=x^{64}-1-x^{64}\\=-1\)
⇒ Giá trị của C không phụ thuộc vào giá trị của biến
a:
Sửa đề: \(P=\left(\dfrac{3+x}{3-x}-\dfrac{3-x}{3+x}-\dfrac{4x^2}{x^2-9}\right):\left(\dfrac{5}{3-x}-\dfrac{4x+2}{3x-x^2}\right)\)\(P=\left(\dfrac{-\left(x+3\right)}{x-3}+\dfrac{x-3}{x+3}-\dfrac{4x^2}{\left(x-3\right)\left(x+3\right)}\right):\dfrac{5x-4x-2}{x\left(3-x\right)}\)
\(=\dfrac{-x^2-6x-9+x^2-6x+9-4x^2}{\left(x-3\right)\left(x+3\right)}:\dfrac{x-2}{x\left(3-x\right)}\)
\(=\dfrac{-4x^2-12x}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x\left(3-x\right)}{x-2}\)
\(=\dfrac{-4x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{-x\left(x-3\right)}{x-2}=\dfrac{4x^2}{x-2}\)
b: x^2-4x+3=0
=>x=1(nhận) hoặc x=3(loại)
Khi x=1 thì \(P=\dfrac{4\cdot1^2}{1-2}=-4\)
c: P>0
=>x-2>0
=>x>2
d: P nguyên
=>4x^2 chia hết cho x-2
=>4x^2-16+16 chia hết cho x-2
=>x-2 thuộc {1;-1;2;-2;4;-4;8;-8;16;-16}
=>x thuộc {1;4;6;-2;10;-6;18;-14}
c: C={0;3;6;9;12;15;18}
c,Theo đầu bài ta có:
x⋮3 và x<20 => x thuộc tập hợp 3,6,9,12,15,18
d,Theo đầu bài ta có:
16⋮x và 0<x<16 => x thuộc tập hợp 4,8