Question

Jika 2x²+3x+5=0
Tentukan x₁/x₂+x₂/x₁ dan x₁³.x₂+x₁.x₂³

Answer 1

2x² + 3x + 5 = 0
x1 + x2 = -b/a = -3/2
x1x2 = c/a = 5/2

x1/x2 + x2/x1
= (x1² + x2²)x1x2
= ((x1 + x2)² - 2x1x2)/x1x2
= ((-3/2)² - 2(5/2))/(5/2)
= (9/4 - 5) x 2/5
= - 11/4 x 2/5
= -11/10

x1³x2 + x1x2³
= x1x2(x1² + x2²)
= x1x2 ((x1+x2)² - 2x1x2)
= 5/2 ((-3/2)² - 2(5/2))
= 5/2 (9/4 - 5)
= 5/2 (-11/4)
= - 55/8

Answer 2

semoga membantu :)