Question

sa se rezolve in R ecuatia
a)I2x +1I=-5
b)IxI=9
c)Ix2+5x +5I=1
x puterea 2+ 5x+5=1
x puterea 2 +5x+5=1

Answer 1

a)I2x +1I=-5
caz 1
2x+1>0
I2x +1I=2x +1
2x+1=-5
2x=-6
x=-3
caz 2
2x+1<0
I2x +1I=-(2x +1)=-2x-1
-2x-1=-5
-2x=-4
x=2

b)IxI=9
x>0         x=9
x<0    IxI=-x    -x=9     x=-9

c)Ix²+5x +5I=1
x²+5x +5>0
Ix²+5x +5I=x²+5x +5
x²+5x +5=1
x²+5x +4=0
x²+4x+x +4=0
x(x+4)+(x +4)=0
(x+4)(x+1)=0
x=-4
x=-1

x²+5x +5<0
Ix²+5x +5I=-x²-5x -5
-x²-5x -5=1
x²+5x +6=0
x²+3x+2x +6=0
x(x+3)+2(x +3)=0
(x+3)(x+2)=0
x=-3
x=-2