Question

1..Rezolva ecuatia-
4/3:x=5/3-1,(3)
2..Completati spatiile punctate
a) Daca 2 la puterea x+1=128 atunci ............,adica..........= x=.....
b) Daca 3 la puterea 2x+1=243,atunci ..........,adica........=x=.......
c) 4/3 ori (-1) la puterea 3 - (-3/5) la puterea -1 + (-1) la puterea 2009/2=.......
3.. Dati 3 exemple de numere rationale care puse in locul lui x sa faca adevarata urmatoarea afirmatie-
|x-2| mai mic sau egal cu 12intregi si 7/12

Answer 1

1)(4/3):x=(5/3)-1,(3)
4/3x=5/3-(13-1)/9
4/3x=5/3-12/9
4/3x=5/3-4/3
4/3x=1/3
4·3=3x
3x=12
x=12/3
x=4

2) 2^(x+1)=128
2^(x+1)=2⁷
x+1=7
x=7-1
x=6

b) 3^(2x+1)=243
3^(2x+1)=3⁵
2x+1=5
2x=5-1
2x=4
x=4/2
x=2

c)(4/3)·(-1)³-(-3/5)⁻¹+(-1)²⁰⁰⁹/2=
-4/3-(-5/3)-1/2=
-4/3+5/3-1/2=
1/3-1/2=(2-3)/6=-1/6

3) Ix-2I≤(12·12+7)/12
Ix-2I≤151/12
cazul I:  x-2=151/12
x=151/12+2=(151+24)/12=176/12=88/6=44/3
x=44/3
cazul II: x-2=-151/12
x=-151/12+2=(-151+24)/12=127/12