Question

Jika diketahui x1 dan x2 merupakan akar-akar persamaan 3x^-2x-8=0, maka tentukan nilai dari :
a. x1+x2
b. x1 x x2
c. (x1)^3 + (x2)^3
d. 1/x1+1/x2

Answer 1

3x² - 2x - 8 = 0

a) x₁ + x₂ = -b/a = 2/3

b) x₁x₂ = c/a = - 8/3

c) x₁³ + x₂³ = (x₁ + x₂)³ - 3x₁x₂(x₁ + x₂)
= 8/27 - 3(-8/3)(2/3)
= 8/27 + 16/3
= (8 + 134)/27
= 142/27

d) 1/x₁ + 1/x₂ = (x₁ + x₂)/x₁x₂
= (2/3)/(-8/3)
= - 1/4

Answer 2

3x² - 2x  - 8 = 0
( 3x + 4) ( x - 2)
x1 = - 4/3    x2 = 2

a . -4/3 + 6/3 = 2/3

b. -4/3* 2 = -8/3

d. -1/ (4/3) + 1/2 = -3/4 + 2/4 = - 1/4


c. -64/27 + 8 = -64/27 + 216/27 = 152/27