Question

2x^2 - 7x + 5 = 0 Trebuie sa se determine solutiile reale ale ecuatiei

Answer 1

2x^2 - 7x + 5 = 0 
Δ = 49 - 4×2×5 = 49 - 40 = 9 
x₁ = (-b+√Δ)/2a = (7 + 3)/4 = 10/2 = 2,5 
x₂ = (-b -√Δ)/2a = (7 - 3)/4 = 4/4 = 1 

S = { 1; 2,5} 

Answer 2

$2 {x}^{2} - 7x + 5 = 0 \\ x = \frac{ - ( - 7) + - \sqrt{ - {7}^{2} - 2 \times x \times 5 } }{4} \\ x = \frac{7 + - \sqrt{9} }{4} \\ x = \frac{7 + - 3}{4}$
Acum ai 2 cazuri:

$x 1= \frac{7 + 3}{4} = \frac{5}{2} \\ x 2= \frac{7 - 3}{4} = 1$
Metoda II:

$2 {x}^{2} - 7x + 5 = 0 \\ 2 {x}^{2} - 2x - 5x + 5 = 0 \\ 2x(x - 1) - 5(x - 1) = 0 \\ (x - 1)(2x - 5) = 0 \\ = > x - 1 = 0 = > x 1= 1 \\ = > 2x - 5 = 0 = > x2 = \frac{5}{2}$