ini gimana cara kerjainnya yah?? (no. 3)

Math Senior High School
Quadratic Equation

Answer :
x² + 8x - 22 = 0

Remember ! Vietta
a + β = -b/a
a + β = -8

a . β = c/a
a . β = -22

So...
x² - (a + 2β + β + 2a)x + [(a + 2β)(2a + β) = 0
x² - (3a + 3β)x + (2a² + 5aβ + 2β²) = 0
x² - [3(a + β)]x + [2(a² + β²) + 5aβ] = 0
x² - [3(-8)]x + [2{a + β)² - 2ab} + 5aβ] = 0
x² + 24x + [2{(-8)² - 2(-22)} + 5(-22)] = 0
x² + 24x + [2{64 + 44} - 110] = 0
x² + 24x + [2(108) - 110] = 0
x² + 24x + 106 = 0

x^2 + 8x - 22 = 0 akar-akarnya a dan b
a + b = x1 + x2 = -b/a = -8/1 = -8
a.b = x1.x2 = c/a = -22/1 = -22

Misal
p = a + 2b dan q = b + 2a
p + q = (a + 2b) + (b + 2a) = 3a + 3b = 3(a + b) = 3(-8) = -24
p.q = (a + 2b)(b + 2a)
= ab + 2a^2 + 2b^2 + 4ab
= 5ab + 2(a^2 + b^2)
= 5ab + 2((a + b)^2 - 2ab)
= 5(-22) + 2((-8)^2 - 2(-22))
= -110 + 2(64 + 44)
= -110 + 2(108)
= -110 + 216
= 106
Jadi persamaan kuadrat yg akar-akarnya (a + 2b) dan (b + 2a) adalah
x^2 - (p + q)x + p.q = 0
x^2 - (-24)x + 106 = 0
x^2 + 24x + 106 = 0

^ = pangkat