Question

multimea solutiilor ecuatiei 5x-10 supra 9 = 20 supra x-2 este: a) {-6;-2} b) {-6;4} c) {-4;8} d) {4;6}.​

Answer 1

Răspuns:

$\frac{5x - 10}{9} = \frac{20}{x - 2} \\ (5x - 10)(x - 2) = 180 \\ 5 {x}^{2} - 20x + 20 = 180 \\ {x}^{2} - 4x + 4 = 36 \\ {x}^{2} - 4x - 32 = 0 \\ delta = 16 + 128 = 144 \: = > \sqrt{delta} = 12$

$x1 = \frac{4 - 12}{2} = - 4 \\ x2 = \frac{4 + 12}{2} = 8$