Question

Tim so nguyen x biet

a) (x - 1)(x + 4) < 0

b) 5^{x + 2}  - 5^{x - 1} = 3100

c) 3^{x + 1} - 3^{x - 2} = 702

Answer 1

a) ( x - 1 )( x + 4 ) < 0

Xét hai trường hợp :

1. \(\hept{\begin{cases}x-1< 0\\x+4>0\end{cases}}\Leftrightarrow\hept{\begin{cases}x< 1\\x>-4\end{cases}}\Rightarrow-4< x< 1\)

2. \(\hept{\begin{cases}x-1>0\\x+4< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}x>1\\x< -4\end{cases}}\)( loại )

Vậy với -4 < x < 1 thì ( x - 1 )( x + 4 ) < 0

b) 5^x+2 - 5^x-1 = 3100

<=> 5^x( 5² - 5^-1 ) = 3100

<=> 5^x( 25 - 1/5 ) = 3100

<=> 5^x.124/5 = 3100

<=> 5^x = 125

<=> 5^x = 5³

<=> x = 3

c) 3^x+1 - 3^x-2 = 702

<=> 3^x( 3 - 3^-2 ) = 702

<=> 3^x( 3 - 1/9 ) = 702

<=> 3^x.26/9 = 702

<=> 3^x = 243

<=> 3^x = 3⁵

<=> x = 5

Answer 2

a) (x - 1)(x + 4) < 0

Xét các trường hợp

TH1\(\hept{\begin{cases}x-1>0\\x+4< 0\end{cases}}\Rightarrow\hept{\begin{cases}x>1\\x< -4\end{cases}}\left(\text{loại}\right)\)

TH2\(\hept{\begin{cases}x-1< 0\\x+4>0\end{cases}}\Rightarrow\hept{\begin{cases}x< 1\\x>-4\end{cases}}\Rightarrow-4< x< 1\left(tm\right)\)

Vậy -4 < x < 1

b) 5^{x + 2} - 5^{x - 1} = 3100

=> 5^x(5² - 1/5) = 3100

=> 5^x.124/5 = 3100

=> 5^x = 125

=> 5^x = 5³

=> x = 3

c) 3^{x + 1} - 3^{x - 2} = 702

=> \(3^x.3-3^x.\frac{1}{3^2}=702\)

=> 3^x(3 - 1/9) = 702

=> 3^x.26/9 = 702

=> 3^x = 243

=> 3^x = 3⁵

=> x = 5

Vậy x = 5

Answer 3

\(\left(x-1\right)\left(x+4\right)< 0\)

\(th1\orbr{\begin{cases}x-1>0\\x+4< 0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x>1\\x< -4\end{cases}\Leftrightarrow1< x< -4\left(1\right)}\)

\(th2\orbr{\begin{cases}x-1< 0\\x+4>0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x< 1\\x>-4\end{cases}\Leftrightarrow-4< x< 1\left(tm\right)}\)

vậy ....

b) \(5^{x+2}-5^{x-1}=3100\)

\(\Leftrightarrow5^x.\left(5^2-5^{-1}\right)=3100\)

\(\Leftrightarrow5^x.\frac{124}{5}=3100\)

\(\Leftrightarrow5^x=125\Leftrightarrow5^x=5^3\Leftrightarrow x=3\)

c)\(3^{x+1}-3^{x-2}=702\)

\(\Leftrightarrow3^x\left(3-3^{-2}\right)=702\)

\(\Leftrightarrow3^x.\frac{26}{9}=702\)

\(\Leftrightarrow3^x=243\Leftrightarrow3^x=3^5\Leftrightarrow x=5\)