Question

Buna.
4.Determina solutiile ecuatiilor:
d)3(x-3)²=48
e)5(x=2)²=45
f)7(2x-1)²=175

7.Determinati x∈ R stiind ca:
b)4x pe 27=3 pe x
e)9 pe 5x=20x pe 4
c)3x pe 16= 1 pe 27x
f)4 pe 6x = 54x pe 25

Answer 1

.Determina solutiile ecuatiilor:
d)3(x-3)²=48
3(x²-6x+9)=48
3x²-18x+27-48=0
3x²-18x-21=0      :3
x²-6x-7=0
Δ=36+28=64
x1=(6-8)/2=-1
x2=(6+8)/2=7
S={-1,7}

e)5(x=2)²=45
5(x²-4x+4)-45=0
5x²-20x+20-45=0
5x²-20x-25=0    :5
x²-4x-5=0
Δ=16+20=36
x1=(4-6)/2=-1
x2=(4+6)/2=5
S={-1,5}

f)7(2x-1)²=175
7(4x²-4x+1)-175=0
28x²-28x+7-175=0
28x²-28x-168=0      :28
x²-x-6=0
Δ=1+24=25
x1=(1-5)/2=-2
x2=(1+5)/2=3
S={-2,3}

7.
b)4x/27=3/ x
4x·x=3·27
4x²=81
x²=81/4
x²=20,25
x1=√20,25=4,5
x2=-4,5

e)9/5x=20x/ 4
9·4=20x·5x
100x²=36
x²=36/100
x1=√36/100=6/10=0,6
x2=-0,6

c)3x/16= 1/27x
3x·27x=16
81x²=16
x²=16/81
x1=√16/81=4/9
x2=-4/9

f)4/ 6x = 54x /25
4·25=54x·6x
324x²=100
x²=100/324
x1=√100/324=10/18
x2=-10/18