Question

Rezolvati in R ecuatia:$2x-\sqrt{x-1}=3$

Answer 1

Răspuns:

2

Explicație pas cu pas:

$x - 1 \geqslant 0 \implies x \geqslant 1$

$2x-\sqrt{x-1}=3$

$2x - 3 = \sqrt{x - 1}$

$\sqrt{x - 1} \geqslant 0 \implies 2x - 3 \geqslant 0 \\ \implies x \geqslant \dfrac{3}{2} \iff x \in \Big[\dfrac{3}{2} ; +\infty \Big)$

$4 {x}^{2} - 12x + 9 = x - 1$

$4 {x}^{2} - 13x + 10 = 0$

$(4x - 5)(x - 2) = 0$

$4x - 5 = 0 \implies x = \dfrac{5}{4} \not \in \Big[\dfrac{3}{2} ; +\infty \Big)$

$x - 2 = 0 \implies x = 2 \in \Big[\dfrac{3}{2} ; +\infty \Big)$

$\implies S = \Big\{2 \Big\}$