Question

tolong dibantu kak saya mau kumpul hari ini, soalnya ada di gambar, tolong ya kak plisss​

Answer 1

Jawab:
a. 1/(x₁) + 1/(x₂) = 5
b. x₁² + x₂² = 29/4
c. (x₁ - x₂)² = 33/4
d. (x₂/x₁) + (x₁/x₂) = -29/2

Penjelasan:
Teori vieta
Ax² + Bx + C = 0
x₁ + x₂ = -B/A
x₁ · x₂ = C/A

Diketahui:
2x² + 5x - 1 = 0
Ax² + Bx + C = 0
A = 2, B = 5, C = -1

Hitunglah
a. 1/(x₁) + 1/(x₂)
= (x₁ + x₂)/(x₁ · x₂)
= (-B/A)/(C/A)
= (-B/A)×(A/C)
= -B/C
= -5/(-1)
= 5

b. x₁² + x₂²
= (x₁ + x₂)² - 2(x₁ · x₂)
= (-B/A)² - 2(C/A)
= (-5/2)² - 2(-1/2)
= (25/4) + 1
= (25/4) + (4/4)
= 29/4

c. (x₁ - x₂)²
= x₁² - 2(x₁ · x₂) + x₂²
= x₁² + x₂² - 2(x₁ · x₂)
= (29/4) - 2(C/A)
= (29/4) - 2(-1/2)
= (29/4) + 1
= (29/4) + (4/4)
= 33/4

d. (x₂/x₁) + (x₁/x₂)
= (x₁² + x₂²)/(x₁ · x₂)
= (29/4)/(C/A)
= (29/4)/(-1/2)
= (29/4) × -2
= -29/2

(xcvi)