Question

Giải phương trình :

\(\dfrac{x+3}{57}+\dfrac{x+4}{28}+\dfrac{x+117}{19}=0\)

Answer 1

\(\frac{x+3}{57}+\frac{x+4}{28}+\frac{x+117}{19}=0\)

⇔\(\left(\frac{x+3}{57}+1\right)+\left(\frac{x+4}{28}+2\right)+\left(\frac{x+117}{19}-3\right)\)= \(0\)

⇔ \(\frac{x+60}{57}+\frac{x+60}{28}+\frac{x+60}{19}=0\)

⇔\(\left(x+60\right)\left(\frac{1}{57}+\frac{1}{28}+\frac{1}{19}\right)=0\)

⇔\(x+60=0\left(do\frac{1}{57}+\frac{1}{28}+\frac{1}{19}>0\right)\)

⇔\(x=-60\)

Vậy S={-60}