Question

Sendo k e p as raizes da equaçao do 2 grau definida por x2_6x+10=0 o valor da expressao e= k+p+k×p+1/k+1/p e:

Answer 1

x² - 6x + 10 = 0

Δ = 6² - 4.1.10

Δ = 36 - 40

Δ = -4           ====>√-4 = ±2i     ====> i² = -1

k = $\frac{6+2i}{2} = 3+i$

p = $\frac{6-2i}{2} = 3-i$

e = (3+i) + (3-i)+ (3+i).(3-i) + $\frac{1}{(3+i)} +  \frac{1}{(3-i)}$

e = 3 + 3 + i - i + 3² + 3i - 3i - i² + $\frac{(3+i)+(3-i)}{3^2 + 3i - 3i - i^2}$

e = 6 + 9 + 1 + $\frac{6}{9 + 1}$

e = 16 + 0,6

e = 16,6