Question

E(x)=4x²-4x+1 supra 2x²-x · 6x+3 supra 8x²-2,x∈ R , \ -1 supra 2 ; 0 ; 1 supra 2 
a)Aratati ca E(x) = 3 supra 2x ,pentru orice x ∈ R \ -1 supra 2 ; 0 ; 1 supra 2 
b)Rezolvati ecuatia E(x)=3 
                   Mersi anticipat . 

Answer 1

E(x)=(2x-1)(2x+1)/x(2x-1)·3(2x+1)/2(4x²-1) simplificam
E(x)=(2x+1)/x·3(2x+1)/2(2x-1)(2x+1) simplificam
E(x)=3(2x+1)/2x(2x-1)
a)E(x)=3/2x
3(2x+1)/2x(2x-1)=3/2x
(6x+3)/(4x²-2x)=3/2x
3·2x(2x+1)=3(4x²-2x)
12x²+6x=12x²-6x
12x²-12x²+6x+6x=0
12x=0
x=0
b)E(x)=3
3(2x+1)/2x(2x-1)=3
6x+3=3·2x(2x-1)
6x+3=12x²-6x
-12x²+6x+6x+3=0
-12x²+12x+3=0        ·(-3)
4x²-4x-1=0
(2x-1)(2x+1)=0
2x-1=0⇒   X1=1/2
2x+1=0⇒  X2=-1/2