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Bài 8: x = 180o - 50o - 45o = 85o
Bài 9: (Bạn ghi rõ đề rồi mik giải nha)
a: |x|=5,6
=>\(\left[{}\begin{matrix}x=5,6\\x=-5,6\end{matrix}\right.\)
c: \(\left|x\right|=3\dfrac{1}{5}\)
=>\(\left|x\right|=3,2\)
=>\(\left[{}\begin{matrix}x=3,2\\x=-3,2\end{matrix}\right.\)
d: |x|=-2,1
mà -2,1<0
nên \(x\in\varnothing\)
d: |x-3,5|=5
=>\(\left[{}\begin{matrix}x-3,5=5\\x-3,5=-5\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=8,5\\x=-1,5\end{matrix}\right.\)
e: \(\left|x+\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
=>\(\left|x+\dfrac{3}{4}\right|=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x+\dfrac{3}{4}=\dfrac{1}{2}\\x+\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=-\dfrac{5}{4}\end{matrix}\right.\)
f: \(\left|4x\right|-\left|-13,5\right|=\left|2\dfrac{1}{4}\right|\)
=>\(4\left|x\right|=2,25+13,5=15,75\)
=>\(\left|x\right|=\dfrac{63}{16}\)
=>\(x=\pm\dfrac{63}{16}\)
g: \(\dfrac{5}{6}-\left|2-x\right|=\dfrac{1}{3}\)
=>\(\dfrac{5}{6}-\left|x-2\right|=\dfrac{1}{3}\)
=>\(\left|x-2\right|=\dfrac{5}{6}-\dfrac{1}{3}=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x-2=\dfrac{1}{2}\\x-2=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{3}{2}\end{matrix}\right.\)
h: \(\left|x-\dfrac{2}{5}\right|+\dfrac{1}{2}=\dfrac{3}{4}\)
=>\(\left|x-\dfrac{2}{5}\right|=\dfrac{3}{4}-\dfrac{1}{2}=\dfrac{1}{4}\)
=>\(\left[{}\begin{matrix}x-\dfrac{2}{5}=\dfrac{1}{4}\\x-\dfrac{2}{5}=-\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}+\dfrac{2}{5}=\dfrac{13}{20}\\x=-\dfrac{1}{4}+\dfrac{2}{5}=\dfrac{-5+8}{20}=\dfrac{3}{20}\end{matrix}\right.\)
i: \(\left|5-3x\right|+\dfrac{2}{3}=\dfrac{1}{6}\)
=>\(\left|3x-5\right|=\dfrac{1}{6}-\dfrac{2}{3}=\dfrac{1}{6}-\dfrac{4}{6}=-\dfrac{3}{6}=-\dfrac{1}{2}< 0\)
=>\(x\in\varnothing\)
k: \(-2,5+\left|3x+5\right|=-1,5\)
=>|3x+5|=-1,5+2,5=1
=>\(\left[{}\begin{matrix}3x+5=1\\3x+5=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-4\\3x=-6\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-\dfrac{4}{3}\\x=-2\end{matrix}\right.\)
m: \(\dfrac{1}{5}-\left|\dfrac{1}{5}-x\right|=\dfrac{1}{5}\)
=>\(\left|\dfrac{1}{5}-x\right|=\dfrac{1}{5}-\dfrac{1}{5}=0\)
=>\(\dfrac{1}{5}-x=0\)
=>\(x=\dfrac{1}{5}\)
n: \(-\dfrac{22}{15}x+\dfrac{1}{3}=\left|-\dfrac{2}{3}+\dfrac{1}{5}\right|\)
=>\(-\dfrac{22}{15}x+\dfrac{1}{3}=\dfrac{2}{3}-\dfrac{1}{5}\)
=>\(-\dfrac{22}{15}x=\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{2}{15}\)
=>-22x=2
=>\(x=-\dfrac{1}{11}\)
\(\frac{1}{4}\) và \(\frac{1}{2}\)
Vì 0x = 0 (Với mọi \(x\in R\)); 12x = 1 (Với mọi \(x\in Z\)).
bài 2
1)
/2x-7/+\(\dfrac{1}{2}=1\dfrac{1}{2}\)
/2x-7/+\(\dfrac{1}{2}=\dfrac{3}{2}\)
/2x-7/=1
=> 2x-7=1 hoặc -2x+7 =1
2x=8 hoặc -2x=-6
x=4 hoặc x=3
Bài 1:
1: Ta có: \(A=\left(-1\right)^3\cdot\left(-\dfrac{7}{8}\right)^3\cdot\left(-\dfrac{2}{7}\right)^2\cdot\left(-7\right)\cdot\left(-\dfrac{1}{14}\right)\)
\(=\dfrac{7^3}{8^3}\cdot\dfrac{4}{49}\cdot\dfrac{1}{2}\)
\(=\dfrac{343}{512}\cdot\dfrac{2}{49}\)
\(=\dfrac{7}{256}\)
Lời giải:
$4+(y-1)^2\geq 4\Rightarrow \frac{8}{4+(y-1)^2}\leq 2$
Mặt khác, áp dụng BĐT $|a|+|b|\geq |a+b|$ ta có:
$|x-1|+|x-3|=|x-1|+|3-x|\geq |x-1+3-x|=2$
$\Rightarrow |x-1|+|x-2|+|x-3|\geq 2+|x-2|\geq 2$
Vậy $\frac{8}{4+(y-1)^2}\leq 2\leq |x-1|+|x-2|+|x-3|$
Dấu "=" xảy ra khi:
\(\left\{\begin{matrix} (y-1)^2=0\\ (x-1)(3-x)\geq 0\\ x-2=0\end{matrix}\right.\Leftrightarrow y=1; x=2\)
để\(\frac{2x-1}{3+x}\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}2x-1< 0\\3+x>0\end{cases}}\\\hept{\begin{cases}2x-1>0\\3+x< 0\end{cases}}\end{cases}}\Leftrightarrow\orbr{\begin{cases}\hept{\begin{cases}x< \frac{1}{2}\\x>-3\end{cases}\left(ktm\right)}\\\hept{\begin{cases}x>\frac{1}{2}\\x< -3\end{cases}\left(tm\right)}\end{cases}}\)
Vậy -3<x<1/2
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