(2x-\(\dfrac{3}{7}\)).(2x\(^2\)+18) = 0
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a) \(\dfrac{x-4}{15}=\dfrac{5}{3}\)
\(\Leftrightarrow x-4=15.\dfrac{5}{3}\)
\(\Leftrightarrow x-4=25\)
\(\Leftrightarrow x=29\) thỏa \(x\inℤ\)
b) \(\dfrac{x}{4}=\dfrac{18}{x+1}\left(x\ne-1\right)\)
\(\Leftrightarrow x\left(x+1\right)=18.4\)
\(\Leftrightarrow x\left(x+1\right)=72\)
vì \(72=8.9=\left(-8\right).\left(-9\right)\)
\(\Leftrightarrow x\in\left\{8;-9\right\}\left(x\inℤ\right)\)
c) \(2x+3⋮x+4\) \(\left(x\ne-4;x\inℤ\right)\)
\(\Leftrightarrow2x+3-2\left(x+4\right)⋮x+4\)
\(\Leftrightarrow2x+3-2x-8⋮x+4\)
\(\Leftrightarrow-5⋮x+4\)
\(\Leftrightarrow x+4\in\left\{-1;1;-5;5\right\}\)
\(\Leftrightarrow x\in\left\{-5;-3;-9;1\right\}\)
=>\(25\cdot\dfrac{\sqrt{a-3}}{5}-7\cdot\dfrac{2}{3}\cdot\sqrt{a-3}-7\sqrt{a^2-9}+18\cdot\dfrac{1}{3}\sqrt{a^2-9}=0\)
=>\(\sqrt{a-3}\cdot\dfrac{1}{3}-\sqrt{a^2-9}=0\)
=>\(\sqrt{a-3}\left(\dfrac{1}{3}-\sqrt{a+3}\right)=0\)
=>a-3=0 hoặc a+3=1/9
=>a=3 hoặc a=-26/9
ĐKXĐ: x>=0; x<>1
PT =>\(\dfrac{\left(\sqrt{x}+3\right)\left(-2x+6\right)}{\left(\sqrt{x}-1\right)^2}=0\)
=>6-2x=0
=>x=3
e: =>2/7-x=2/5
=>7-x=5
=>x=2
f: =>2x+3/3=10/3
=>2x+3=10
=>2x=7
=>x=7/2
g: =>(14+x)/7=15/7
=>x+14=15
=>x=1
h: =>(2x+3)/x=13/x
=>2x+3=13
=>2x=10
=>x=5
Tính M = \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\)
a: =>4x-6-9=5-3x-3
=>4x-15=-3x+2
=>7x=17
hay x=17/7
b: \(\Leftrightarrow\dfrac{2}{3x}-\dfrac{1}{4}=\dfrac{4}{5}-\dfrac{7}{x}+2\)
=>2/3x+21/3x=4/5+2+1/4=61/20
=>23/3x=61/20
=>3x=23:61/20=460/61
hay x=460/183
a: ta có: \(2\left(4-3x\right)+2x=5\left(2x-3\right)\)
\(\Leftrightarrow8-6x+2x-10x+15=0\)
\(\Leftrightarrow-14x=-23\)
hay \(x=\dfrac{23}{14}\)
b: Ta có: \(\dfrac{1}{2}-\left(2x-\dfrac{1}{3}\right)^2=\dfrac{7}{18}\)
\(\Leftrightarrow\left(2x-\dfrac{1}{3}\right)^2=\dfrac{1}{9}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{1}{3}=\dfrac{1}{3}\\2x-\dfrac{1}{3}=-\dfrac{1}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{2}{3}\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=0\end{matrix}\right.\)
\(a;-\frac{3}{9}+\frac{7}{15}=-x+\left(-\frac{5}{18}\right)\)
\(\Rightarrow\frac{2}{15}=-x-\frac{5}{18}\)
\(\Rightarrow-x=\frac{2}{15}+\frac{5}{18}=\frac{37}{90}\)
\(b;2x-\frac{3}{4}=x-\frac{1}{2}\)
\(\Rightarrow2x-x=-\frac{1}{2}+\frac{3}{4}\)
\(\Rightarrow x=\frac{1}{4}\)
a)-3/9+7/15=-x+(-5/18) b)2x-3/4= x-1/2
=>-x+(-7/15)=2/15 =>2x-x=3/4-1/2
=>-x=2/15-(-7/15) =>x=1/4
=>-x=3/5
=>x=+3/5
\(=>\left[{}\begin{matrix}2x-\dfrac{3}{7}=0\\2x^2+18=0\left(>0\forall x\right)\end{matrix}\right.=>2x-\dfrac{3}{7}=0\\ =>2x=\dfrac{3}{7}\\ =>x=\dfrac{3}{14}\)
\(\left(2x-\dfrac{3}{7}\right).\left(2x^2+18\right)=0\)
Ta có : \(x^2\ge0\Rightarrow2x^2+18>0\)( với mọi x )
\(\Rightarrow2x-\dfrac{3}{7}=0\)
\(\Leftrightarrow x=\dfrac{3}{14}\)