Question

Mă poate ajuta cineva şi la asta? Mulțumesc!​

Answer 1

Cazul 1: $a \neq -\frac{15}{16}$

$\frac{2}{5}(3 - \frac{8}{3}x) = a^{-1}x \vert \cdot 15$

$6(3-\frac{8}{3}x) = 15a^{-1}x\\18 - 16x = 15a^{-1}x\\x(15a^{-1} + 16) = 18$

$x = \frac{18}{15a^{-1} + 16}$

Cazul 2: $a = -\frac{15}{16} \implies a^{-1} = -\frac{16}{15}$

$18 - 16x = 15a^{-1}x \iff 18 - 16x = 15 \cdot (-\frac{16}{15})x \iff 18 - 16x = -16x \implies x \in \O$