Question

Afla x∈R din :
a) 2 - x/2 = 3 + x/2 + 4 ;
b) 4x - x + 1/6 = 2x/6 - 1/6
c) 16x + 2/9 - x+1/3 = -x + 1
d) 1 + 2x-1/3 - 2 intregi si 1/9=2,0(5)
f) 1,1(6)x - 2 intregi si 1/2(x + 2) = 5x - 9
k) (x - √3)² - (x - √2) (x + √2) = x + 1
m) √(0,25 - 1/4x)² = 0,75

Answer 1

a . 2 - 3-4 = x/2 +x/2  ;   x =  -5
b.  4x  -x/3  = -1/6 -1/6    ; ( 12x - x) / 3 = -2/6 ;  11x  = -1    ;  x = - 1/11
c. 16x  = 1  -2/9  -1/3    ;  16x =  4/9    ; x =1/ 36
d. 2x = 37 /18  -1 + 1/3 +19/9   ;   2x = 63 / 18  ; x =  7 /4 
f . 7/6 - 5/2 ( x +2 )  = 5x -9   ; 7 -15x -30 = 30x  -54   ; -21 +54 =45x  ; x=11/15
k.     x² -2 √3x +3  - x² +2 =x +1   ;   x ( 2√3 +1) =  4   ; x =4( 2√3  -1 )  /11

Answer 2

a) 2 - x/2 = 3 + x/2 + 4
-x/2-x/2=-2+3+4
-2x/2=5
-x=5    inmultim -1
x=-1

b) 4x - x + 1/6 = 2x/6 - 1/6 
3x-2x/6=-1/6-1/6
(18x-2x)/6=-2/6                  ·6 si simplificam
18x-2x=-2
16x=-2
x=-2/16
x=-1/8
x=-0,125

c) 16x + 2/9 - x+1/3 = -x + 1
15x+x=1-2/9-1/3
16x=(9-2-3)/9
16x=4/9
16x·9=4
144x=4
x=4/144=2/72=1/36

d) 1 + 2x-1/3 - 2 intregi si 1/9=2,0(5)
2,0(5)=(205-20)/90=185/90=37/18
1+2x-1/3-19/9=37/18
2x=37/18-1+1/3+19/9
2x=(37-18+6+38)/18
2x=63/18
2x·18=63
36x=63
x=63/36
x=1,75

f) 1,1(6)x - 2 intregi si 1/2(x + 2) = 5x - 9
1,1(6)=(116-11)/90=105/90=21/18=7/6
7x/6-5/2(x+2)=5x-9
7x/6-5x/2-10/2=5x-9
7x/6-5x/2-5x=-9+5
(7x-15x-30x)/6=-4
-38x=-4·6     inmultim -1
38x=24
x=24/38=12/19

k) (x - √3)² - (x - √2) (x + √2) = x + 1 
x²-2√3x+3-(x²-2)=x+1
x²-2√3x+3-x²+2=x+1
-2√3x-x=1-5
-2√3x-x=-4    inmultim -1
2√3x+x=4
x(2√3+1)=4
x=4/(2√3+1)=4(2√3-1)/(12-1)=4(2√3-1)/11

m) √(0,25 - 1/4x)² = 0,75
0,25-x/4=0,75
-x/4=0,75-0,25
-x/4=0,5    inmultim -1
x=-0,2·4
x=-2