Question

Tìm x biết

a) ( 5x-1)(2x-1/3)=0

b) ( x^2+1)(x-4) =0

c) 2x^2-1/3x=0

d) (4/5)^5.X=(4/5)^7

e)Tìm X ∈ Z để A= X+5/X-2 có giá trị nguyên

Answer 1

e)

A = \(\frac{x+5}{x-2}\) = \(\frac{\left(x-2\right)+7}{x-2}=1+\frac{7}{x-2}\)

Muốn A nguyên thì:

=> \(\frac{7}{x-2}\) ∈ Z

=> 7 ⋮ x - 2

=> x - 2 ∈ Ư (7)

=> x - 2 ∈ { 1; 7; -1; -7 }

=> x ∈ { 3; 9; -5; 1 }

Answer 2

a) (5x - 1)(2x - 1/3) = 0

\(\Rightarrow5x-1=0\) hoặc \(2x-\frac{1}{3}=0\)

\(\Rightarrow\left[{}\begin{matrix}5x=0+1\\2x=0+\frac{1}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}5x=1\\2x=\frac{1}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1:5=\frac{1}{5}\\x=\frac{1}{3}:2=\frac{1}{3}.\frac{1}{2}=\frac{1}{6}\end{matrix}\right.\)

Vậy x = 1/5 hoặc x = 1/6