jika akar-akar persamaan kuadrat 3x²+5x+1=0 adalah α dan β, maka nilai 1/α² + 1/β² sama dengan ...

jawab

3x² + 5x + 1= 0
a = 3
b = 5
c = 1

α+β = -b/a = - 5/3
α β = c/a = 1/3

p = 1/α² + 1/β²
p= (α²+ β²)/(α β)²
p= {(α+β)²- 2 αβ} /(αβ)²
p= {(-5/3)² - 2(1/3)} / (1/3)²
p = (25/9 - 2/3) /(1/9)
p = 9 ( 25/9 - 2/3)
p = 25 - 6
p = 19
=