Giải phương trình:
a) x-1/59 + x-2/58 + x-3/57 = x-4/56 + x-5/55 + x-6/54
b) 59-x/41 + 57-x/43 + 55-x/45 = -3
c) x+14/86 + x+15/85 + x+16/84 + x+17/83 + x+116/4 = 0
d) x-90/10 + x-76/12 + x-58/14 + x-36/16 + x-15/17 = 15
Giải phương trình: a) x-1/59 + x-2/58 + x-3/57 = x-4/56 + x-5/55 + x-6/54 b) 59-x/41 + 57-x/43 + 55-x/45 = -3 c) x+14/86 + x+15/85 + x+16/84 + x+17/83
By Peyton
Đáp án:
a, x−1/59+x−2/58+x−3/57=x−4/56+x−5/55+x−6/54⇒(x−1/59−1)+(x−2/58−1)+(x−3/57−1)=(x−4/56−1)+(x−5/55−1)+(x−6/54−1)
⇒x−60/59+x−60/58+x−60/57=x−60/56+x−60/55+x−60/54
⇒x−60/59+x−60/58+x−60/57−x−60/56−x−60/55−x−60/54=0
⇒(x−60) (1/59+1/58+1/57−1/56−1/55−1/54)=0Vì1/59+1/58+1/57−1/56−1/55−1/54≠0suy rax−60=0⇔x=60
c,
x+14/86+x+15/85+x+16/84+x+17/83+x+11/64=0
x+14/86+x+15/85+x+16/84+x+17/83+x+11/64=0
⇔x+14/86+1+x+15/85+1+x+16/84+1+x+17/83+1+x+11/64−4=0
⇔x+14/86+1+x+15/85+1+x+16/84+1+x+17/83+1+x+11/64−4=0
⇔x+100/86+x+100/85+x+100/84+x+100/83+x+100/4=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
⇔(x+100)(1/86+1/85+1/84+1/83+1/4)=0
⇔x+100=0
⇔x+100=0.
Do 186+185+184+183+14≠0186+185+184+183+14≠0
⇔x=−100
d, x−90/10+x−7612+x−5814+x−3616+x−1517=15
⇔(x−90/10−1)+(x−76/12−2)+(x−58/16−3)+(x−36/16−4)+(x−15/17−5)=0
⇔x−100/10+x−100/12+x−100/14+x−100/16+x−100/17=0
⇔(x−100).(1/10+1/12+1/14+1/16+1/17)=0⇔x−100=0(Vì:1/10+1/12+1/14+1/16+1/17≠0)
⇔x=100
,b, (59-x)/41+(57-x)/43+(55-x)/45=-3
(59-x)/41 +1+ (57-x)/43 + 1+(55-x)/45 + 1
=-3+3=0 (cộng 2 vế với 3)
=> (100-x)/41+(100-x)/43+(100-x)/45=0
=> (100-x)(1/41+1/43+1/45)=Vì 1/41+…+1/45>0
=> 100-x=0 =>x=100