jika akar akar persamaan kuadrat 3x² + 5x + 1 = 0 adalah α dan β maka nilai[tex] \frac{1}{ \alpha ^{2} } + \frac{1}{ \beta ^{2} } [/tex] adalah

alpha = a
betha = b

3x² + 5x + 1 = 0
a + b = -5/3
ab = 1/3

(1/a²) + (1/b²)
= (a² + b²)/(ab)²
= ((a + b)² - 2ab)/(ab)²
= ((25/9) - (6/9))/(1/9)
= 25 - 6
= 19

Mapel : Matematika
Kelas : X SMA
Materi : Persamaan Kuadrat

Pembahasan :
3x² + 5x + 1 = 0

Berdasarkan Teorema Vietta
α + β = -b/a
α + β = -5/3

αβ = c/a
αβ = 1/3

Maka...
1/α² + 1/β²
= (α² + β²)/(α²β²)
= [(α + β)² - 2αβ]/(αβ)²
= [(-5/3)² - 2(1/3)]/(1/3)²
= [25/9 - 2/3]/(1/9)
= [19/9]/(1/9)
= (19 x 9)/(1 x 9)
= (19 x 1)/1
= 19