Question

Se considera ecuatia $x^{2}$ - 8x + 20=0 cu radacini x1, x2 ∈ R. Calculati x1² + x2², $\frac{1}{x1}$ + $\frac{1}{x2}$

Dau coroana!!!!!

Answer 1

x²-8x+20 = 0

=> x² = 8x-20

=> x₁²+x₂² = (8x₁-20)+(8x₂-20) =

= 8(x₁ + x₂) - 40 = 8•8 - 40 = 24

x²-8x+20 = 0|:x (x ≠ 0)

x-8+20/x = 0

20/x = 8-x

1/x = (8-x)/20

=> 1/x₁ + 1/x₂ = (8-x₁)/20 + (8-x₂)/20 =

= (16 -(x₁ + x₂))/20 = (16+8)/20 =

= 24/20 = 12/10 = 6/5