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Bài 1:
a: f(0)=1
f(2)=-3x2+1=-6+1=-5
f(-2)=-3x2+1=-5
f(-1/2)=-3x1/2+1=-3/2+1=-1/2
b: f(x)=-3
=>-3|x|+1=-3
=>-3|x|=-4
=>|x|=4/3
=>x=4/3 hoặc x=-4/3
\(a,\frac{1}{2}x+\frac{5}{2}=\frac{7}{2}x-\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{2}x+\frac{5}{2}-\frac{7}{2}x=-\frac{3}{4}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{7}{2}x+\frac{5}{2}=-\frac{3}{4}\)
\(\Leftrightarrow-3x+\frac{5}{2}=-\frac{3}{4}\)
\(\Leftrightarrow-3x=-\frac{13}{4}\)
\(\Leftrightarrow x=-\frac{13}{4}:(-3)=-\frac{13}{4}:\frac{-3}{1}=-\frac{13}{4}\cdot\frac{-1}{3}=\frac{13}{12}\)
\(b,\frac{2}{3}x-\frac{2}{5}=\frac{1}{2}x-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{3}x-\frac{2}{5}-\frac{1}{2}x=-\frac{1}{3}\)
\(\Leftrightarrow\frac{2}{3}x-\frac{1}{2}x-\frac{2}{5}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{6}x-\frac{2}{5}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{6}x=\frac{1}{15}\)
\(\Leftrightarrow x=\frac{1}{15}:\frac{1}{6}=\frac{1}{15}\cdot6=\frac{6}{15}=\frac{2}{5}\)
\(c,\frac{1}{3}x+\frac{2}{5}(x+1)=0\)
\(\Leftrightarrow\frac{1}{3}x+\frac{2}{5}x+\frac{2}{5}=0\)
\(\Leftrightarrow\frac{11}{15}x=-\frac{2}{5}\)
\(\Leftrightarrow x=-\frac{6}{11}\)
d,e,f Tương tự
Ta có :
\(\left(2x^2-3x+1\right)-\left(2x^2-3x+4\right)=0\)
\(\Leftrightarrow2x^2-3x+1-2x^2+3x-4=0\)
\(\Leftrightarrow-3=0\left(ktm\right)\)
\(\Leftrightarrow x\in\varnothing\)
a, 3 - 2 | 5x - 4 | = -11
2|5x - 4| = 14
|5x - 4| = 7
Th1: 5x -4 =7
5x = 11
x= 11/5
Th2:
5x -4 =-7
5x = -3
x= -3/5
a) => 2/5x-4/=14
=> /5x-4/=7
=> 5x-4=7 hoac 5x-4=-7
x=11/5 x=-3/5
/5x-4/=/x+2/
\(\orbr{\begin{cases}5x-4=x+2\\5x-4=-x+2\end{cases}}suyra\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{1}{2}\end{cases}}\)
vậy x=3/2 hoặc x=1/2
a) \(2x^2+x-6=0\Leftrightarrow2x^2+4x-3x-6=0\)
\(\Leftrightarrow2x\left(x+2\right)-3\left(x+2\right)=0\Leftrightarrow\left(2x-3\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2x=3\\x=-2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\x=-2\end{matrix}\right.\)
vậy \(x=\dfrac{3}{2};x=-2\)
b) \(-5x^2+17x-6=0\Leftrightarrow-5x^2+15x+2x-6=0\)
\(\Leftrightarrow-5x\left(x-3\right)+2\left(x-3\right)\Leftrightarrow\left(-5x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}-5x+2=0\\x-3=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}5x=2\\x=3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{5}\\x=3\end{matrix}\right.\)
vậy \(x=\dfrac{2}{5};x=3\)
c) \(3x^2+22x-16=0\Leftrightarrow3x^2+24x-2x-16=0\)
\(\Leftrightarrow3x\left(x+8\right)-2\left(x+8\right)=0\Leftrightarrow\left(3x-2\right)\left(x+8\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-2=0\\x+8=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x=2\\x=-8\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\x=-8\end{matrix}\right.\)
vậy \(x=\dfrac{2}{3};x=-8\)
d) \(2x^3+3x^2-8x+3=0\Leftrightarrow2x^3-3x^2+x+6x^2-9x+3=0\)
\(\Leftrightarrow x\left(2x^2-3x+1\right)+3\left(2x^2-3x+1\right)=0\Leftrightarrow\left(x+3\right)\left(2x^2-3x+1\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(2x^2-2x-x+1\right)=0\Leftrightarrow\left(x+3\right)\left(2x\left(x-1\right)-\left(x-1\right)\right)=0\)
\(\left(x+3\right)\left(2x-1\right)\left(x-1\right)=0\) \(\Leftrightarrow\left\{{}\begin{matrix}x+3=0\\2x-1=0\\x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-3\\2x=1\\x=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-3\\x=\dfrac{1}{2}\\x=1\end{matrix}\right.\) vậy \(x=-3;x=\dfrac{1}{2};x=1\)
Toán lớp 6 nhé mn nhấn lộn!hihi