Question

Rezolvati ecuatia
9x^2-30x+25=1

Answer 1

$9x^2-30x+25=1 \Rightarrow (3x-5)^2 = 1 \\ \\ Notam: 3x-5 = t \\ \\ \Rightarrow t^2 = 1 \Rightarrow t = \pm 1 \\ \\ \boxed{1} \quad t = 1 \Rightarrow 3x-5 = 1 \Rightarrow 3x = 6 \Rightarrow \boxed{x = 2} \\ \\ \boxed{2} \quad t = -1 \Rightarrow 3x-5 = -1 \Rightarrow 3x = 5-1 \Rightarrow 3x = 4 \Rightarrow \boxed{x = \dfrac{4}{3}} \\ \\ \\ \Rightarrow S = \Big\{\dfrac{4}{3},2\Big\}$