Question

Jika alpha (a) dan beta (b) akar-akar persamaan kuadrat 3x²-6x-1=0, nilai dari (a/b + b/a) adalah...

a. -4
b. -8
c. -14
d. -20
e. -22
​

Answer 1

Jawaban:

C -14

Penjelasan dengan langkah-langkah:

[tex] \alpha + \beta = \frac{b}{a} = \frac{ - ( - 6)}{3} = 2 \\ \alpha \times \beta = \frac{c}{a} = \frac{ - 1}{3} \\ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ { \alpha \beta } } = \frac{ {( \alpha + \beta )}^{2} - 2 \alpha \beta }{ \alpha \beta } \\ = \frac{ {( 2)}^{2} - 2( - \frac{1}{3} )}{ - \frac{1}{3} } = 4 \frac{2}{3} \times - \frac{3}{1} = - 14[/tex]