Question

Calculati valoarea expresieia
a)$\frac{ a^{3}-1 }{2a ^{3} } * \frac{5a ^{2} }{ a^{2} +a+1}$ daca a =-3
b)$\frac{ a^{2}-4 }{ a^{2}-3a+9 } ; \frac{a+2}{ a^3+27}$ daca a=0,5

Answer 1

a=0,5 =1/2
(a³-1)/2a³ * 5a²/(a²+a+1) =
=(a-1)(a²+ab+1)/2a³ * 5a²/(a²+a+1) =
=5(a-1)/2a 

5(a-1)/2a = 5(1/2-1) / 2*1/2 = 
=5(-1/2) =-2,5 

(a²-4)/(a²-3a+9) :( a+2) /(a³+27) =
=(a+2)(a-2)/(a²-3a+9) * (a+1)(a²-3a+9)/( a+2) =
=(a-2)(a+1)  

(a-2)(a+1)  = (0,5-2)(0,5+1) = (-1,5)(1,5)=-2,25