Question

Giải phương trình sau : \(\frac{29-x}{21}+\frac{27-x}{23}+\frac{25-x}{25}+\frac{23-x}{27}+\frac{21-x}{29}=-5\)

Answer 1

\(pt\Leftrightarrow\frac{29-x}{21}+1+\frac{27-x}{23}+1+...=0\)

\(\Leftrightarrow\frac{50-x}{21}+\frac{50-x}{23}+\frac{50-x}{25}+\frac{50-x}{27}+\frac{50-x}{29}=0\)

\(\Leftrightarrow\left(50-x\right)\left(\frac{1}{21}+\frac{1}{23}+\frac{1}{25}+\frac{1}{27}+\frac{1}{29}\right)=0\)

Do \(\frac{1}{21}+\frac{1}{23}+\frac{1}{25}+\frac{1}{27}+\frac{1}{29}>0\) nên 50 - x = 0 hay x = 50.

Answer 2

pt<=>29-x/21+1+27-x/23+1+...=0

<=>50-x/21+50-x/23+50-x/25+50-x/27+50-x/29=0

<=>(50-x).(1/21+1/23+1/25+1/27+1/29)=0

Do 1/21+1/23+1/25+1/27+1/29>0 nên 50-x=0 hay x=50