TESTUL1
1a)12-x=-3 ⇒-x=-3-12 inmultim cu -1 ⇒ x=15
b)1/3·x-1/4=0 ⇒ x/3=1/4⇒⇒4x=3⇒ x=3/4
c)√2x+√2-x=2-√2⇒ ⇒√2x-x=2-√2-√2
x(√2-1)=2-2√2⇒ x=-2(√2-1)/(√2-1)⇒ x=-2
2) (x-3)²/3-(1-x)(x+1)/2=(5x-1)(x+2)/6-3
(x²-6x+9)/3-(x+1-x²-x)/2=(5x²+10x-x-2)/6-3 aducem la acelasi numitor care e 6
2(x²-6x+9)-3(1-x²)=5x²+9x-2-3·6
2x²-12x+18-3+3x²=5x²+9x-20
5x²-5x²-12x-9x=-20-15
-21x=-35 inmultim cu -1
x=35/21⇒
x=1,(6)
5) a+b+c=30
b=6+a, c=(a+b)/4=(a+6+a)/4=(2a+6)/4=2(a+3)/4 simplificam
c=(a+3)/2
inlocuim a+6+a+(a+3)/2=30⇒2a+(a+3)/2=30-6 aducem la acelasi numitor
(4a+a+3)/2=24⇒ ( 5a+3)=24·2
5a=48-3⇒⇒ a=45/5⇒ a=9
b=6+9=15
c=(9+3)/2=12/2=6
TESTUL 2
1a)5x+2x=9x⇒ 7x-9x=0-2x=0⇒ x=0
b) 1/4-x=0,1⇒ -x=1/10-1/4 ·(-1)⇒aducem la acelasi numitor
x=-1/10+1/4⇒ x=(-4+10)/40⇒ x=6/40 simplifcam x=3/20
x=0,15
c)x+(2+√3)=2x-(2-√3)
x-2x=-2-√3+2+√3
-x=0⇒ x=0
2) 1,(3)=(13-1)/9=12/9=4/3 copiezi ezercitiul si
⇒x-(x-2)/3-(x²-8x+16)/9-6=[(x√2/3-4/3)(x√2/3+4/3)] aducem la acelaasi numitor
[9x-3x+6-x²+8x-16-54)/9=(2x²+4√2x-4√2x-16)/3
(-x²+14x-64)/9=(2x²-16)/3 aducem la acelasi numitor
(-x²+14x-64)=6x²-48
-x²-6x²+14x-64+48=0
-7x²+14x-14=0 inmultim cu -1
7(x²-2x+2)=0
x²-2x+2=0
Testul 3
1a)x-√5=5
x=5+√5
b)7-4x=35
-4x=35-7
-4x=28 ·(-1)
x=28/4⇒ x=7
c)0,2x+0,03=0,004
0,2x=0,004-0,03
0,2x=-0,026
x=-0,026/0,2=-26/1000:2/10
x=-260/2000
x=-0,13
2) copiezi ex⇒x²-4x/9+4/9+3=x-x/3-4/9+x²+4x/3
x²-x²-4x/9-x+x/3-4x/3=-4/9-4/9-3
-4x/9-x-3x/3=-8/9-3 aducem la acelasi numitor
(-4x-9x-9x)/9=(-8-9)/9
-22x=-17 inmultim cu -1
x=17/22
x=0,7(72)
