Question

$\left \{\atop \right. 16^x=48y \\ \\ \left \{\atop \right. 4^x=3y$

Rezolvati in R×R sistemul de ecuatii:

Answer 1

Din ec a doua $y=\dfrac{4^x}{3}$, care inlocuita in prima ec. da

$4^{2x}=48\cdot\dfrac{4^x}{3}\Rightarrow 4^{2x}=4^2\cdot4^x\Rightarrow 4^{2x}=4^{x+2}\Rightarrow 2x=x+2\Rightarrow x=2$.

Acum $y=\frac{4^2}{3}=\frac{16}{3}$