Question

3 la puterea 8 minus 3 la puterea 6 egal cu x la puterea 3
A.x<15
B.x=16
C.x=17
D.x>sau egal 18

Answer 1

[tex] 3^{8} - 3^{6} = x^{3} ( 3^{2} -1 )*3^6 =x^3 (9-1)*3^6=x^3 8*3^6=x^3 x^3=8*3^6 x^3=8*729 x^3=5832 x^3=18^3 x=18 [/tex]

Answer 2

$3^{8}-3^{6}= \text{x}^3\\ \\ 3^6\cdot(3^2-1) = \text{x}^3 \\ \\ 3^{6}\cdot (9-1) = \text{x}^3 \\ \\ 3^6\cdot 8 = \text{x}^3 \\ \\ {(3^2)}^3\cdot 2^3 = \text{x}^3 \\ \\ 9^3\cdot 2^3 = \text{x}^3 \\ \\ (9\cdot 2)^3 = \text{x}^3 \\ \\ 18^3 = \text{x}^3 \\ \\ \Rightarrow \boxed{\text{x} = 18} \quad atunci cand x apartine \mathbb_{R} .$