Jika a dan b akar persamaan kuadrat 3x²-2x-4=0 nilai dari 1/α²+1/β²?​

X² – 2x – 4 = 0

α + β = -b/a = -(-2)/1 = 2

α x β = c/a = -4/1 = -4
.

1/α² + 1/β²

= β²/α²β² + α²/α²β²

= (β² + α²)/(αβ)²

= [(α + β)² – 2αβ]/(αβ)²

= [(2)² – 2(-4)]/(-4)²

= (4 + 8)/16

= 12/16

= 3/4