Question

Fie x,y € R, astfel incat 2x-3y= -5 si 4x^2- 9y^2=20. Determinati. 2x+ 3y
(€= apartine). Va rog ajutati-ma!

Answer 1

$2x-3y=-5 \\ 2x+3y=? \\ \\ \\ 4x^2-9y^2=20 \Rightarrow \big(2x+3y\big)\cdot \big(2x-3y\big) = 20 \Rightarrow \\ \Rightarrow (2x+3y)\cdot (-5) = 20 \Rightarrow 2x+3y = \dfrac{20}{-5} \Rightarrow \boxed{2x+3y = -4}$