Question

Scrieti ecuatiile in multimea numerelor  retionale:
a) 3x+12/3=2x+52/6
b)42-2/5x=77/15
c)32/5x-11/2=x-27/10
d)(23/4-31/2):(x-2)=12/8
e)(x-13/4):(15/4-23/4)=11/3
f)3/10+3x-2/4=13/1--2x-4/5
g)(x-2)·11/2+15/6=21/6x-52/3
h)1/8(19+3x)=1/5-14/5x

Answer 1

*- inmultire; /-impartire
a) se inmultesc in cruce => 6(3x+12)=3(2x+52)
18x+72=6x+156
18x-6x=156-72
12x=84
x=7
b)40/5x=77/15 se inmultesc in cruce => 600=385x , si nu merge, cred ca ai mancat un x pe undeva
c) 32/5x-11*1/2=x-27/10
32/10x-22=x-27/10 se inmultesc in cruce => 320=(10x-22)(x-27)
320= 10x^2-270x-22x+594
10x^2-292x+274=0
delta=b^2-4ac= 85264-10960=74304 nu are solutii
d) se umplifica 31/2 cu 2, pentru a avea numitor comun, si anume 4=> (32-62/4):(x-2)=12/8
-30/4*1/x-2=12/8
-30/4x-8=12/8
-240=48x-96
48x=-96+240
48x=144
x=3
e)x-13/4:(-8/4)= 11/3
x-13/4:(-1/2)=11/3
-x+13/8=11/3
88=-3x+39
3x=88-39
3x=49