Question

Answer 1

a. \(\dfrac{2}{3}+x:\dfrac{3}{7}=\dfrac{4}{15}\)

<=> \(x.\dfrac{7}{3}=-\dfrac{2}{5}\)

<=> \(x=-\dfrac{6}{35}\)

b. Tương tự a

c. \(\dfrac{x-3}{x-5}=\dfrac{5}{7}\left(ĐK:x\ne5\right)\)

<=> 7(x - 3) = 5(x - 5)

<=> 7x - 21 = 5x - 25

<=> 2x = - 4

<=> x = -2 (TM)

d. 5.2^x + 4.2^x = 72

<=> 2^x(5 + 4) = 72

<=> 2^x.9 = 72

<=> 2^x = 8

<=> x = 3

e. (x + 2)³ = -125

<=> (x + 2)³ + 5³ = 0

<=> \(\left(x+7\right)\left[\left(x+2\right)^2-5\left(x+2\right)+25\right]=0\)

<=> \(\left[{}\begin{matrix}x+7=0\\\left(x+2\right)^2-5\left(x+2\right)+25=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=-7\\x=VNghiệm\end{matrix}\right.\)

 

g. (2x - 1)² = 81

<=> (2x - 1)² - 9² = 0

<=> (2x - 1 + 9)(2x - 1 - 9) = 0

<=> (2x + 8)(2x - 10) = 0

<=> \(\left[{}\begin{matrix}2x+8=0\\2x-10=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=-4\\x=5\end{matrix}\right.\)

h. \(\left|x+\dfrac{1}{3}\right|-4=1\)

<=> \(\left[{}\begin{matrix}x+\dfrac{1}{3}-4=1\\-x-\dfrac{1}{3}-4=1\end{matrix}\right.\) 

<=> \(\left[{}\begin{matrix}x=\dfrac{14}{3}\\x=-\dfrac{16}{3}\end{matrix}\right.\)

k. Tương tự h

o. 4^{x + 2} + 4^{x + 1} - 4^x = 176

<=> 4^x(4² + 4 - 1) = 176

<=> 4^x.19 = 176

<=> 4^x = \(\dfrac{176}{19}\) (Vô lí)

Vậy nghiệm của PT là \(S=\varnothing\)