Question

Rezolvati in Z ecuatiile:
a)23(2x -5) +41(3x +7) - 115= -20(x +11) +15(4x +7)+43;
b)10 • {2x + [3(x - 5)-2(-x +7)]+3(2x -5)} +20=150;
c)x +2x +4x +…+2048x =2 la puterea 13 - 2;
d) (-3x +9)(2x -4)=0;
e) (2x -4)(-5x +10)(3x +7)=0

Answer 1

a)23(2x -5) +41(3x +7) - 115= -20(x +11) +15(4x +7)+43
46x -115 +123x +287 - 115= -20x -220 +60x +105+43
169x   +57 = 40x -72
129x=-129
x=-1

b)10 • {2x + [3(x - 5)-2(-x +7)]+3(2x -5)} +20=150
10 • [2x + (3x - 15+2x-14+6x -15)] =150-20
10 • (2x +11x - 44) =130
13x - 44=13
13x =57
x=19

c)x +2x +4x +…+2048x =2¹³ - 2
x(1 +2 +4 +8+16+32+64+128+256+512+1024+2048) =2¹³ - 2
x×4095 =8192 - 2
x×4095 =8190
x=2

d) (-3x +9)(2x -4)=0
-3x+9=0  x=9/3=3
2x-4=0  x=2

e) (2x -4)(-5x +10)(3x +7)=0
2x-4=0  x=2
-5x+10=0  x=2
3x+7=0  x=-7/3