Question

Giải phương trình:

a) $x^{3}=2;$

b) $27 x^{3}=-81;$

c) $\dfrac{1}{2} x^{3}=0,4$;

d) $\sqrt[3]{3 x+1}=4;$

e) $\sqrt[3]{3-2 x}=-3;$

f) $\sqrt[3]{x-2}+2=x$.

Answer 1

a) x^{3}=2 \Leftrightarrow x=\sqrt[3]{2}x3=2⇔x=32​.

b) 27 x^{3}=-81 \Leftrightarrow x^{3}=-3 \Leftrightarrow \sqrt[3]{x^{3}}=\sqrt[3]{-3} \Leftrightarrow x=-\sqrt[3]{3}27x3=−81⇔x3=−3⇔3x3​=3−3​⇔x=−33​.

c) \dfrac{1}{2} x^{3}=0,004 \Leftrightarrow x^{3}=0,008 \Leftrightarrow \sqrt[3]{x^{3}}=\sqrt[3]{0,008} \Leftrightarrow x=0,2 .21​x3=0,004⇔x3=0,008⇔3x3​=30,008​⇔x=0,2.

d) \sqrt[3]{3 x+1}=4 \Leftrightarrow 3 x+1=4^{3} \Leftrightarrow x=21.33x+1​=4⇔3x+1=43⇔x=21.

e) \sqrt[3]{3-2 x}=-3 \Leftrightarrow 3-2 x=(-3)^{3} \Leftrightarrow x=15.33−2x​=−3⇔3−2x=(−3)3⇔x=15.

f) \sqrt[3]{x-2}+2=x \Leftrightarrow \sqrt[3]{x-2}=x-2 \Leftrightarrow x-2=(x-2)^{3}.3x−2​+2=x⇔3x−2​=x−2⇔x−2=(x−2)3.

\Leftrightarrow(x-2)\left[(x-2)^{2}-1\right]=0 \Leftrightarrow\left[\begin{array}{l}x-2=1 \\ (x-2)^{2}=1\end{array}\Leftrightarrow\left[\begin{array}{l}x=2 \\ x-2=1 \\ x-2=-1\end{array}\Leftrightarrow\left[\begin{array}{l}x=2 \\ x=3 \\x=1\end{array}\right.\right.\right..⇔(x−2)[(x−2)2−1]=0⇔⎣⎢⎡​x−2=1(x−2)2=1​⇔⎣⎢⎡​x=2x−2=1x−2=−1​⇔⎣⎢⎡​x=2x=3x=1​.

Answer 2

a) x=\(\sqrt[3]{2}\)         b x=\(\sqrt[3]{-3}\)     c) x=0,2       d)x=21       e) x=15      f) x=3

Answer 3

a) $x^3=2\iff x=\sqrt[3]{32}$.

b) $27x^3=-81\iff x^3=-3\iff \sqrt[3]{3x^3}=\sqrt[3]{3-3}\iff x=-\sqrt[3]{33}$.

12x3=0,004⇔x3=0,008⇔3√x3=3√0,008⇔x=0,2.12x3=0,004⇔x3=0,008⇔x33=0,0083⇔x=0,2.

d) $\sqrt[3]{33x+1}=4\iff 3x+1=4^3\iff x=21.$

e) $\sqrt[3]{33-2x}=-3\iff 3-2x=(-3{)}^3\iff x=15.$

f) $\sqrt[3]{3x-2}+2=x\iff \sqrt[3]{3x-2}=x-2\iff x-2=(x-2{)}^3.$

$\iff (x-2)\left[(x-2{)}^2-1\right]=0\iff [\begin{array}{c}x-2=1\\ (x-2{)}^2=1\end{array}\iff [\begin{array}{c}x=2\\ x-2=1\\ x-2=-1\end{array}\iff [\begin{array}{c}x=2\\ x=3\\ x=\mathrm{1v}\end{array}$

Answer 4

a) $x^3=2\iff x=\sqrt[3]{32}$.

b) $27x^3=-81\iff x^3=-3\iff \sqrt[3]{3x^3}=\sqrt[3]{3-3}\iff x=-\sqrt[3]{33}$.

12x3=0,004⇔x3=0,008⇔3√x3=3√0,008⇔x=0,2.12x3=0,004⇔x3=0,008⇔x33=0,0083⇔x=0,2.

d) $\sqrt[3]{33x+1}=4\iff 3x+1=4^3\iff x=21.$

e) $\sqrt[3]{33-2x}=-3\iff 3-2x=(-3{)}^3\iff x=15.$

f) $\sqrt[3]{3x-2}+2=x\iff \sqrt[3]{3x-2}=x-2\iff x-2=(x-2{)}^3.$

$\iff (x-2)\left[(x-2{)}^2-1\right]=0\iff [\begin{array}{c}x-2=1\\ (x-2{)}^2=1\end{array}\iff [\begin{array}{c}x=2\\ x-2=1\\ x-2=-1\end{array}\iff [\begin{array}{c}x=2\\ x=3\\ x=\mathrm{1v}\end{array}$

Answer 5

a, \(\sqrt[3]{2}\)

b, \(-\sqrt[3]{3}\)

c, 0,2

d,21

e,15

d, 2,3,1

Answer 6

a)x=∛2³    b)x=∛-3³    c)x=∛0,8³     d)x=21     e)x=15    f)x=2

Answer 7

a) x=3√2

b) x=-3√3

c) x=0,2

d) x=21

e) x=15

f) x=2; x=3; x=1

Answer 8

3can2

-3can3

0,2

21

15

(x-2)^3

2,3,1

Answer 9

a) ∛2

b) -∛3

c) 0,2

d) 21

e) 15

f) 2, 3, 1

Answer 10

a) x=³√2

b) x=³√-3

c) x=³√4/5

d) x=21

e) x=-15

f) 

 

Answer 11

a. \(\sqrt[3]{2}\)

b. \(\sqrt[3]{-3}\)

c. 0,2

d. 21

e. 15

f. 3

Answer 12

a, x^3=2<=> x= căn bậc ba của 2

b, 27x^3=21<=>x^3=-3 <=> căn bậc ba x^3= căn bậc ba-3

   <=> x= - căn bậc ba 3

c, 1/2x^3=0,004<=>x^3=0,008<=> căn bậc ba x^3=căn bậc ba 0,008<=>x=0,2

d, Căn bậc ba 3x+1=4<=>3x+1=4^3<=> x=21

e,Căn bậc ba 3-3x = -3 <=> x-2x=(-3)^3 <=> x=15

f, Căn bậc ba x-2 +2=x <=> căn bậc ba x-2 = x-2

<=>x-2=(x-2)^3<=> (x-2)[(x-2)^2-1]=0

<=>x-2=1 <=>x=2

      (x-2)^2=1<=>x-2=1;x-2=-1<=>x=3;x=1

 

Answer 13

\(x^3=2\Rightarrow x=\sqrt[3]{2}\)

\(27x^3=-81\Rightarrow3x=\sqrt[3]{-81}\)

\(\dfrac{1}{2}x^3=0.4\Rightarrow\dfrac{1}{8}x=\sqrt[3]{0.4}\)\(\sqrt[3]{x-2}+2=x\Rightarrow x-2+8=x^3\)

\(\sqrt[3]{3x+1}=4\Rightarrow\left(\sqrt[3]{3x+1}\right)^3=64\)

\(\sqrt[3]{3-2x}=-3\Rightarrow\left(\sqrt[3]{3-2x}\right)^3=-27\)

Answer 14

  

Answer 15

\(x^3=2\Leftrightarrow x=\sqrt[3]{2}\)
\(27x^3=-81\Leftrightarrow x^3=-3\Leftrightarrow\sqrt[3]{x^3}=\sqrt[3]{-3}\Leftrightarrow x=-\sqrt[3]{3}\)
\(\dfrac{1}{2}x^3=0,004\Leftrightarrow x^3=0,008\Leftrightarrow\sqrt[3]{x^3}=\sqrt[3]{0,008\Leftrightarrow x}=0,2\)
\(\sqrt[3]{3x+1}=4\Leftrightarrow3x+1=4^3\Leftrightarrow x=21\)
\(\sqrt[3]{3-2x}=-3\Leftrightarrow3-2x=\left(-3\right)^3\Leftrightarrow x=15\)

\(\sqrt[3]{x-2}+2=x\Leftrightarrow\sqrt[3]{x-2}=x-2\Leftrightarrow x-2=\left(x-2\right)^3\Leftrightarrow\left(x-2\right)[\left(x-2\right)^2-1]=0\Leftrightarrow\left[{}\begin{matrix}x-2=1\\\left(x-2\right)^2=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x-2=1\\x-2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)