Question

Jika Akar PK 4x² - x + 2 = 0 adl α & β
Tentukan
a) α+β
b) α.β
c) α/β + β/α
d) 1/α-2 + 1/β-2

Beserta Caranya Yaaa....

Makasih ...

Answer 1

A= 4 ,  b = -1 , c = 2
a. α + β = -b/a = -(-1)/4 = 1/4
b. αβ = c/a = 2/4 = 1/2
c. α/β + β/α = α²/αβ + β²/αβ = (α² + β²) / αβ
   = ((α + β)² - 2αβ) / αβ = ((1/4)² - 2(1/2) / 1/2
  = (1/16 - 1) / 1/2
  = -15/16    /  1/2
  = -30/16
d. 1/α-2 + 1/β-2 = ( (β - 2) + (α-2)) / (α-2)(β - 2)
   =  (α + β - 4) / (αβ - 2 (α+β) + 4)
   = (1/4 - 4 ) / (1/2 - 2 (1/4) +4)
   = -3/4  /  4
  = -3 / 16