Question

persamaan kuadrat x ^ 2 - 2x + 1 = 0 mempunyai akar-akar x1 dan x2 persamaan kuadrat yang akar-akarnya 2/x1 + 2/x2 dan x1/x2 + x2/x1 adalah​

Answer 1

Jawaban:

x = 4 dan x = 2

(x - 4)(x - 2) = 0

x² - 6x + 8 = 0 ....(B)

Penjelasan dengan langkah-langkah:

x² - 2x + 1 = 0

a= 1

b= -2

c= 1

(x1 + x2) = -b/a = 2/1 = 2

(x1.x2) = c/a = 1

[tex] \frac{2}{x1} + \frac{2}{x2} = \frac{2x2 +2x1 }{(x1.x2)} \\ = \frac{2(x1 + x2)}{(x1.x2)} \\ = \frac{2(2)}{1} \\ = 4[/tex]

[tex] \frac{x1}{x2} + \frac{x2}{x1} = \frac{ {(x1)}^{2} + (x2 {)}^{2} }{(x1.x2)} \\ = \frac{(x1 + x2 {)}^{2} - (2x1.x2) }{(x1.x2)} \\ = \frac{(2 {)}^{2} - 2(1)}{1} \\ = 4 - 2 \\ = 2[/tex]