Question

1)tìm x biết:

a)(x-2)^2=1

b)(2x-1)^3=-8

c)(x+1/2)^2=1/16

d)(x-2)^3=-27

e(2x-3)^2=25

g)3^x-1=1/243

h)2^x+2^x+3=144

k)81^-2x*27^x=95

 

Answer 1

a. (x - 2)² = 1

<=> (x - 2)² = 1² = (-1)²

<=> \(\begin{cases}x-2=1\\x-2=-1\end{cases}\Leftrightarrow\begin{cases}x=3\\x=1\end{cases}\)

Vậy x \(\in\){1; 3}.

b. (2x - 1)³ = -8

<=> (2x - 1)³ = (-2)³

<=> 2x - 1 = -2

<=> 2x = -2 + 1

<=> 2x = -1

<=> x = -1/2

Vậy x = -1/2.

c. (x + 1/2)² = 1/16

<=> (x + 1/2)² = (1/4)² = (-1/4)²

<=> \(\begin{cases}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{cases}\Leftrightarrow\begin{cases}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{cases}\)

Vậy x \(\in\){-1/4; -3/4}.

d. (x - 2)³ = -27

<=> (x - 2)³ = (-3)³

<=> x - 2 = -3

<=> x = -3 + 2

<=> x = -1

Vậy x = -1.

Answer 2

a.\(\left(x-2\right)^2\)=1

<=> x-2=1 hoặc x-2=-1

<=> x= 3 hoặc x=1

b.\(\left(2x-1\right)^3\)=-8

\(\left(2x-1\right)^3\)=\(\left(-2\right)^3\)

2x-1=-2

2x=-1

x=-1/2

c.\(\left(x+\frac{1}{2}\right)^2\)=\(\frac{1}{16}\)

\(\left(x+\frac{1}{2}\right)^2\)=\(\left(\frac{1}{4}\right)^2\)hoặc \(\left(x+\frac{1}{2}\right)^2\)=\(\left(-\frac{1}{4}\right)^2\)

x+\(\frac{1}{2}\)=\(\frac{1}{4}\)  hoặc x+\(\frac{1}{2}\)=-\(\frac{1}{4}\)

x=-\(\frac{1}{4}\)hoặc x=-\(\frac{3}{4}\)

d.\(\left(x-2\right)^3\)=-27

\(\left(x-2\right)^3\)=\(\left(-3\right)^3\)

x-2=-3

x=-1

Answer 3

g.\(3^{x-1}\)=\(\frac{1}{243}\)

\(3^{x-1}\)=\(\frac{1}{3^5}\)

\(3^{x-1}\)=\(3^{-5}\)

x-1=-5

x=-4

Answer 4

e. (2x - 3)² = 25

<=> (2x - 3)² = 5² = (-5)²

<=> \(\begin{cases}2x-3=5\\2x-3=-5\end{cases}\)<=> \(\begin{cases}2x=8\\2x=-2\end{cases}\)<=> \(\begin{cases}x=4\\x=-1\end{cases}\)

Vậy x \(\in\){-1; 4}.

g. 3^x-1 = 1/243

<=> 3^x-1 = 3^-5

<=> x - 1 = -5

<=> x = -5 + 1

<=> x = -4

Vậy x = -4.

h. 2^x + 2^x+3 = 144

<=> 2^x.(1 + 2³) = 144

<=> 2^x . 9 = 144

<=> 2^x = 16

<=> 2^x = 2⁴

<=> x = 4

Vậy x = 4.

h. 81 ^ ?