X *2 1/2 +X*1/2 = 27
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1/
\(3\left(-1-4x^2+5x\right)+4\left(3x^2+7x-6\right)=-27\)
\(\Leftrightarrow-3-12x^2+15x+12x^2+28x-24=-27\)
\(\Leftrightarrow43x=0\Rightarrow x=0\)
2/
\(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x^2-1\right)=27\)
\(\Leftrightarrow x^3+27-x^3+x=27\)
\(\Leftrightarrow x=0\)
a. \(lim_{x\rightarrow3}\dfrac{x^3-27}{3x^2-5x-2}=\dfrac{3^3-27}{3.3^2-5.3-2}=\dfrac{0}{10}=0\)
b. \(lim_{x\rightarrow2}\dfrac{\sqrt{x+2}-2}{4x^2-3x-2}=\dfrac{\sqrt{2+2}-2}{4.2^2-3.2-2}=\dfrac{0}{8}=0\)
c. \(lim_{x\rightarrow1}\dfrac{1-x^2}{x^2-5x+4}=lim_{x\rightarrow1}\dfrac{\left(1-x\right)\left(x+1\right)}{\left(x-1\right)\left(x-4\right)}=lim_{x\rightarrow1}\dfrac{-\left(x+1\right)}{x-4}=\dfrac{-\left(1+1\right)}{1-4}=\dfrac{2}{3}\)
d. Câu này mình chịu, nhìn đề hơi lạ so với bình thường hehe
\(=\dfrac{3}{2}\cdot\dfrac{4}{2}\cdot\dfrac{5}{3}\cdot\dfrac{6}{4}\cdot...\cdot\dfrac{27}{25}\cdot\dfrac{28}{26}\cdot\dfrac{29}{27}\)
\(=\dfrac{1}{4}\cdot28\cdot29=7\cdot29=203\)
a: \(27^{2-x}< =9\)
=>\(\left(3^3\right)^{2-x}< =3^2\)
=>\(3^{6-3x}< =3^2\)
=>6-3x<=2
=>-3x<=-4
=>\(x>=\dfrac{4}{3}\)
b: \(7^{3-x}< 49\)
=>\(7^{3-x}< 7^2\)
=>3-x<2
=>-x<2-3=-1
=>x>1
c: \(27^{3-x}>9\)
=>\(\left(3^3\right)^{3-x}>3^2\)
=>\(3^{9-3x}>3^2\)
=>9-3x>2
=>-3x>-7
=>\(x< \dfrac{7}{3}\)
d: \(2^{3-x}< 2^3\)
=>3-x<3
=>-x<0
=>x>0
e: \(27^{3-x^2}< 27^{x+1}\)
=>\(3-x^2< x+1\)
=>\(-x^2-x+2< 0\)
=>\(x^2+x-2>0\)
=>(x+2)(x-1)>0
=>\(\left[{}\begin{matrix}x>1\\x< -2\end{matrix}\right.\)
b) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2=\left(\pm\frac{1}{4}\right)^2\)
\(\Rightarrow x+\frac{1}{2}=\pm\frac{1}{4}.\)
\(\Rightarrow\left[{}\begin{matrix}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{4}-\frac{1}{2}\\x=\left(-\frac{1}{4}\right)-\frac{1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{-\frac{1}{4};-\frac{3}{4}\right\}.\)
c) \(\left(3x+2\right)^3=-27\)
\(\Rightarrow\left(3x+2\right)^3=\left(-3\right)^3\)
\(\Rightarrow3x+2=-3\)
\(\Rightarrow3x=\left(-3\right)-2\)
\(\Rightarrow3x=-5\)
\(\Rightarrow x=\left(-5\right):3\)
\(\Rightarrow x=-\frac{5}{3}\)
Vậy \(x=-\frac{5}{3}.\)
Chúc bạn học tốt!
a) \(\left(x-\frac{1}{2}\right)^3=27\)
=> \(\left(x-\frac{1}{2}\right)^3=3^3\)
=> \(x-\frac{1}{2}=3\)
=> \(x=3+\frac{1}{2}\)
=> \(x=\frac{7}{2}\)
Vậy \(x=\frac{7}{2}.\)
b) \(\left(2x-1\right)^3=-27\)
=> \(\left(2x-1\right)^3=\left(-3\right)^3\)
=> \(2x-1=-3\)
=> \(2x=\left(-3\right)+1\)
=> \(2x=-2\)
=> \(x=\left(-2\right):2\)
=> \(x=-1\)
Vậy \(x=-1.\)
Chúc bạn học tốt!