_____Giải phương trình sau______
$\frac{x-5}{100}$+ $\frac{x-4}{101}$+ $\frac{x-3}{102}$= $\frac{x-100}{5}$+ $\frac{x-101}{4}$ +$\frac{x-102}{3}$
_____Giải phương trình sau______
$\frac{x-5}{100}$+ $\frac{x-4}{101}$+ $\frac{x-3}{102}$= $\frac{x-100}{5}$+ $\frac{x-101}{4}$ +$\frac{x-102}{3}$
Đáp án:
x=150
Giải thích các bước giải:
$\frac{x-5}{100}$ +$\frac{x-4}{101}$ +$\frac{x-3}{102}$=$\frac{x-100}{5}$+ $\frac{x-101}{4}$+ $\frac{x-102}{3}$
⇔($\frac{x-5}{100}$-1)+( $\frac{x-4}{101y}$-1)+( $\frac{x-3}{102}$-1) =($\frac{x-100}{5}$-1)+( $\frac{x-101}{4}$-1)+( $\frac{x-102}{3}$-1)
⇔$\frac{x-105}{100}$+ $\frac{x-105}{101}$+$\frac{x-105}{102}$ =$\frac{x-105}{5}$+ $\frac{x-105}{4}$+ $\frac{x-105}{3}$
⇔(x-150).($\frac{1}{100}$ +$\frac{1}{101}$+ $\frac{1}{102}$ – $\frac{1}{5}$ – $\frac{1}{4}$ -$\frac{1}{3}$ )=0
⇔x-150=0 (thấy ($\frac{1}{100}$ +$\frac{1}{101}$+ $\frac{1}{102}$ – $\frac{1}{5}$ – $\frac{1}{4}$ -$\frac{1}{3}$ $\neq$ 0)
⇒x=150
vậy x=150
Đáp án:Xin hay nhất !!!
Giải thích các bước giải:
`(x-5)/100+(x-4)/101+(x-3)/102=(x-100)/5+(x-101)/4+(x-102)/3`
`=>((x-5)/100-1)+((x-4)/101-1)+((x-3)/102-1)=((x-100)/5-1)+((x-101)/4-1)+((x-102)/3-1)`
`=>(x-105)/100+(x-105)/101+(x-105)/102-(x-105)/5-(x-105)/4-(x-105)/3=0`
`=>(x-105).(1/100+1/101+1/102-1/5-1/4-1/3)=0`
`=>x-105=0`
Vì `(1/100+1/101+1/102-1/5-1/4-1/3)\ne0`
`=>x=105`