Question

Sendo x1 e x2 raízes da equação 2x²-5x-1=0, calcule o valor de x1²+x2²

Answer 1

   2x² - 5x - 1 = 0
  Δ = b² - 4ac = 25 + 8 = 33
 √Δ = +-√33

x1 = (5+√33)/4
x2 = (5-√33)/4

(x1)² = [(5+√33)/4]² = (25+10√33+33)/16
(x2)² = [(5- √33)/4]² = (25- 10√33+33)/16

(x1)² + (x2)² =
(25 + 10√33 + 33 + 25 - 10√33 + 33)/16 = 116/16 = 29/4