Đáp án:
31, `x=-100`
32, `x=100`
33, `x=1995`
34, `x=-100`
Giải thích các bước giải:
31,
`(x+14)/86+(x+15)/85+(x+16)/84+(x+17)/83=-4`
`<=>((x+14)/86+1)+((x+15)/85+1)+((x+16)/84+1)+((x+17)/83+1)=0`
`<=>(x+100)/86+(x+100)/85+(x+100)/84+(x+100)/83=0`
`<=>(x+100)(1/86+1/85+1/84+1/83)=0`
Nhận thấy:
`1/86+1/85+1/84+1/83\ne0`
`=>x+100=0`
`<=>x=-100`
Vậy `S={-100}`
32,
`(59-x)/41+(57-x)/43+(55-x)/45+(53-x)/47=-4`
`<=>((59-x)/41+1)+((57-x)/43+1)+((55-x)/45+1)+((53-x)/47+1)=0`
`<=>(100-x)/41+(100-x)/43+(100-x)/45+(100-x)/47=0`
`<=>(100-x)(1/41+1/43+1/45+1/47)=0`
Nhận thấy:
`1/41+1/43+1/45+1/47\ne0`
`=>100-x=0`
`<=>x=100`
Vậy `S={100}`
33,
`(x-5)/1990+(x-15)/1980+(x-25)/1970=(x-1990)/5+(x-1980)/15+(x-1970)/25`
`<=>((x-5)/1990-1)+((x-15)/1980-1)+((x-25)/1970-1)=((x-1990)/5-1)+((x-1980)/15-1)+((x-1970)/25-1)`
`<=>(x-1995)/1990+(x-1995)/1980+(x-1995)/1970=(x-1995)/5+(x-1995)/15+(x-1995)/25`
`<=>(x-1995)/1990+(x-1995)/1980+(x-1995)/1970-(x-1995)/5-(x-1995)/15+(x-1995)/25=0`
`<=>(x-1995)(1/1990+1/1980+1/1970-1/5-1/15-1/25)=0`
Nhận thấy:
`1/1990<1/25=>1/1995-1/25<0`
`1/1980<1/15=>1/1980-1/15<0`
`1/1970<1/5=>1/1970-1/5<0`
`=>1/1990+1/1980+1/1970-1/5-1/15-1/20<0`
`=>x-1995=0`
`<=>x=1995`
Vậy `S={1995}`
34,
`(x+14)/86+(x+15)/85+(x+16)/84+(x+17)/83+(x+116)/4=0`
`<=>((x+14)/86+1)+((x+15)/85+1)+((x+16)/84+1)+((x+17)/83+1)+((x+116)/4-4)=0`
`<=>(x+100)/86+(x+100)/85+(x+100)/84+(x+100)/83+(x+100)/4=0`
`<=>(x+100)(1/86+1/85+1/84+1/83+1/4)=0`
Nhận thấy:
`1/86+1/85+1/84+1/83+1/4\ne0`
`=>x+100=0`
`<=>x=-100`
Vậy `S={-100}`
