giải phương trình sau : x-13/501+x-17/2000=x-15/1001+x-16/667 16/07/2021 Bởi Rose giải phương trình sau : x-13/501+x-17/2000=x-15/1001+x-16/667
$\frac{x-13}{501}+$ $\frac{x-17}{2000}=$ $\frac{x-15}{1001}+$ $\frac{x-16}{667}$ $⇔(\frac{x-13}{501}-4)+($ $\frac{x-17}{2000}-1)-($ $\frac{x-15}{1001}-2)-($ $\frac{x-16}{667}-3)=0$ $⇔\frac{x-2017}{501}+$ $\frac{x-2017}{2000}-$ $\frac{x-2017}{1001}-$ $\frac{x-2017}{667}=0$ $⇔(x-2017)(\frac{1}{501}+$ $\frac{1}{2000}-$ $\frac{1}{1001}-$ $\frac{1}{667})=0$ $⇔x-2017=0$ (Vì:$\frac{1}{501}+$ $\frac{1}{2000}-$ $\frac{1}{1001}-$ $\frac{1}{667})$$\neq$ 0) ⇔x=2017 Vậy S={2017} Bình luận
$\frac{x-13}{501}+$ $\frac{x-17}{2000}=$ $\frac{x-15}{1001}+$ $\frac{x-16}{667}$
$⇔(\frac{x-13}{501}-4)+($ $\frac{x-17}{2000}-1)-($ $\frac{x-15}{1001}-2)-($ $\frac{x-16}{667}-3)=0$
$⇔\frac{x-2017}{501}+$ $\frac{x-2017}{2000}-$ $\frac{x-2017}{1001}-$ $\frac{x-2017}{667}=0$
$⇔(x-2017)(\frac{1}{501}+$ $\frac{1}{2000}-$ $\frac{1}{1001}-$ $\frac{1}{667})=0$
$⇔x-2017=0$ (Vì:$\frac{1}{501}+$ $\frac{1}{2000}-$ $\frac{1}{1001}-$ $\frac{1}{667})$$\neq$ 0)
⇔x=2017
Vậy S={2017}
Đáp án:
x= 2017
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