Question

Cateva probleme, daca vreti puteti sa-mi si explicati cum rezolvati, multumesc!!

1. f(x) = x+1 ; g(x) = 2-3x
Det. x apartine R pentru care |f(x)-g(x)| = |f(x)+g(x)|

2. Rez. in multimea nr reale ecuatia Logaritm in baza 2 din (x la puterea 2 + 7) = 4

3. Calculati |a-1| + |a+1| unde a = 1 supra 1 + radical din 2

4.

Answer 1

1) Ix+1-2+3xI=Ix+1+2-3xI
I4x-1I=I-2x+3I
4x-1=0
x1=1/4
-2x+3=0
-2x=-3     inmultim -1
x2=3/2
x          -α                    1/4                3/2                         +α
4x-1     - - - - - - - - -- - - -0+++++++++++++++++++++++++++
-2x+3   - - - - - - - - - - - - - - - - - - - - - - -0+++++++++++++++++
           + +++++++++++0- - - - - - - - - -0++++++++++++++++
daca x∈(-α,1/4]=D1
-4x+1=2x-3
-4x-2x=-3-1
-6x=-4               inmultim -
6x=4
x=4/6=2/3∉D1
daca x∈(1/4,3/2)=D2
4x-1=2x-3
4x-2x=1-3
2x=-2
x=-2/2=-1∈D2
daca x∈[3/2,+α)=D3
4x-1=-2x+3
4x+2x=3+1
6x=4
x=4/6=2/3∉D3
x∈Ф

3)a=1/(1+√2)=(1-√2)/(1-2)=√2-1
Ia-1I+Ia+1I=I√2-1-1I+I√2-1+1)=I√2-2I+I√2I=2-√2+√2=2