1) a) cond.x≠-75
x+5=0
x=-5
b) cond 8x-16≠0⇒ 8x≠16⇒ x≠16/8⇒ x≠2
x+11=0
x=-11
2a) a²=0
a₁=a₂=0
b) x-3=0
x₁=3
x-4=0
x₂=4
S={3,4}
d) Δ=49-4·12=49-48=1
x₁=(7+1)/2=8/2=4
x₂=(7-1)/2=6/2=3
S={3,4}
d) 9x²+6x+1=15x-1
9x²+6x+15x+1+1=0
9x²+21x+2=0
Δ=441-4·19·2=441-152=289
x₁=(-21+17)/2·9=-4/18=-2/9=-0,(2)
x₂=(-21-17)/18=-39/18=-2,1(6)
S={-0,(2); -2,1(6)}
3)S=x₁+x₂=-3-5=-8
P=x₁·x₂=(-3)(-5)=15
x²-Sx+P=0
x²-(-8)x+15=0
x²+8x+15=0
4) {x+y=7
{-x+7y=9
x-x+y+7y=7+9
8y=16
y=16/8
y=2
din x+y=7 rezulta x+2=7
x=7-2
x=5
5) {15x-6x<13+8
{12x-9x>7-18
{9x<21
{3x>-11
{x<21/9 simplif.cu 3 rezulta x<7/3
{x>-11/3
-∞ -11/3 7/3 +∞
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x∈(-11/3,7/3)
6) {x+y=100 inmultim cu -3
{3x+4y=340
notam cu x ap.cu 3 camere si cu y ap.cu 4 camere
{-3x-3y=-300
{3x+4y=340
3x-3x+4y-3y=340-300
y=40 deci sunt 40 ap.cu 4 camere
din x+y=100 rezulta x+40=100
x=100-40
x=60 deci 60 ap.cu 3 camere
7) x+y+z+w=360
{x,y,z,w}dp {2,3,6,7}
x/2=y/3=z/6=w/7=k
x=2k
y=3k
z=6k
w=7k
2k+3k+6k+7k=360
18k=360
k=360/18
k=20
x=2k=2·20=40
x=40
y=3k=3·20
y=60
z=6k=6·20
z=120
w=7k=7·20
w=140
40+60+120+140=360
