Question

Giải các phương trình sau:

9) x-49/ 50 + x-50/ 49 = 49/ x-50 + 50/ x-49

7) x+25/ 75 + x+30/70 = x+35/65 + x+40/60

8) 99-x/101 + 97-x/103 + 95-x/105 + 93-x/107 = 4

10) x+14/86 + x+15/85 + x+16/84 + x+17/83 + x+116/4 = 0

Answer 1

9: \(\dfrac{x-49}{50}+\dfrac{x-50}{49}=\dfrac{49}{x-50}+\dfrac{50}{x-49}\)

=>x-99=0

hay x=99

7: \(\Leftrightarrow\left(\dfrac{x+25}{75}+1\right)+\left(\dfrac{x+30}{70}+1\right)=\left(\dfrac{x+35}{65}+1\right)+\left(\dfrac{x+40}{60}+1\right)\)

=>x+100=0

hay x=-100

8:

Sửa đề: \(\dfrac{99-x}{101}+\dfrac{97-x}{103}+\dfrac{95-x}{105}+\dfrac{93-x}{107}=-4\) 

\(\Leftrightarrow\left(\dfrac{99-x}{101}+1\right)+\left(\dfrac{97-x}{103}+1\right)+\left(\dfrac{95-x}{105}+1\right)+\left(\dfrac{93-x}{107}+1\right)=0\)

=>200-x=0

hay x=200