jika α dan β adalah akar akar persamaan kuadrat 2x²-5x+6=0, nilai[tex] \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } [/tex] = mohon di bantu ya

Kelas 10 Matematika
Bab Persamaan Kuadrat

2x² - 5x + 6 = 0
a = 2; b = -5; c = 6

α/β + β/α
= (α² + β²)/(αβ)
= ((α + β)² - 2αβ)/(αβ)
= ((-b/a)² - 2 . c/a) / (c/a)
= ((5/2)² - 2 . 6/2) / (6/2)
= (25/4 - 6) / 3
= (25/4 - 24/4) / 3
= 1/12

2x^2 - 5x + 6 = 0

[tex]2x^2 - 5x + 6 = 0 \\ \\ \alpha + \beta = \frac{ - b}{a} = \frac{5}{2} \\ \\ \alpha \beta = \frac{c}{a} = \frac{6}{2} = 3 \\ \\ \frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ \\ \frac{( \alpha + \beta {)} ^{2} - 2 \alpha \beta }{3} \\ \\ \frac{ (\frac{5}{2} {)}^{2} - 2(3) }{3} \\ \\ \frac{ \frac{25}{4} - 6 }{3} \\ \\ \frac{ \frac{1}{4} }{3} \\ \\ \frac{3}{4} = = > > [/tex]


mohon untuk diperiksa terlebih dahulu