Persamaan kuadrat x2-3x+1=0 mempunyai akar-akar α dan β maka nilai ( a2-a+1) (β2+β+1)=...

Pers. Kuadrat

• a+b = 3
• a.b = 1
• a-b = -√D/a = √-3²-4(1)(1) / 1 = √5
...
(a²-a+1)(b²+b+1)
= a²b²+a²b+a²-ab²-ab-a+b²+b+1
= a²b²+a²b-ab²+a²+b²-ab-a+b+1
= (ab)²+ab(a-b)+[(a+b)²-2ab]-ab-a+b+1
= (1)²+(1)(√5)+(3)²-2(1)-(1)-(3)+1
= 5+√5