Question

Tìm x , biết :

a) \(\left(\frac{1}{7}x-\frac{2}{7}\right)\left(\frac{-1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)

b) \(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

Answer 1

\(a,\left(\frac{1}{7}x-\frac{2}{7}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)

TH1 : \(\frac{1}{7}x-\frac{2}{7}=0\Rightarrow\frac{x-2}{7}=0\Rightarrow x-2=0\Leftrightarrow x=2\)

TH2 : \(-\frac{1}{5}x+\frac{3}{5}=0\Rightarrow\frac{-x+3}{5}=0\Rightarrow-x+3=0\Leftrightarrow x=3\)

TH3 : \(\frac{1}{3}x+\frac{4}{3}=0\Rightarrow\frac{x+4}{3}=0\Rightarrow x+4=0\Leftrightarrow x=-4\)

\(\Rightarrow x\in\left\{2;3;-4\right\}\)

Answer 2

\(b,\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

\(\Rightarrow\frac{5}{30}x+\frac{3}{30}x-\frac{8}{30}x+1=0\)

\(\Rightarrow\frac{5x+3x-8x}{30}+1=0\)

\(\Rightarrow1=0\)( vô lý )\(\Rightarrow x\in\varnothing\)

Answer 3

a) (1/7x - 2/7)(-1/5x + 3/5)(1/3x + 4/3) = 0

3 trường hợp:

TH1: 1/7x - 2/7 = 0 <=> 1/7x = 0 + 2/7 <=> 1/7x = 2/7 <=> x = 2.7/7 = 2

=> x = 2

TH2: -1/5x + 3/5 = 0 <=> -1/5x = 0 - 3/5 <=> -1/5x = -3/5 <=> x = (-3/5).(-5) = 3

=> x = 3

TH3: 1/3x + 4/3 = 0 <=> 1/3x = 0 - 4/3 <=> 1/3x = -4/3 <=> x = x = 3.(-4/3) = -4

=> x = -4

Vậy: x = 2, 3, -4

b) 1/6x + 1/10x - 4/15x + 1 = 0

<=> 1/6x + 1/10x - 4/15x = 0 - 1

<=> 1/6x + 1/10x - 4/15x = -1

<=> 1/6x.30 + 1/10x.30 - 4/15x.30 = -1.30

<=> 5x + 3x - 8x = -30

<=> 0 = -30

=> không có x thỏa mãn