Soal UN Matematika IPA 2015 No 6

Jawaban Soal UN Matematika IPA 2015
Soal UN Matematika IPA 2015

6. Persamaan kuadrat -2x² + 3x - 2 = 0 memiliki akar - akar x₁ dan x₂, nilai dari x₁³ + x₂³ = ...

A. 9/8
B. 3/8
C. - 1/8
D. - 3/8
E. - 9/8

Jawaban : E
-2x² + 3x - 2 = 0
a = -2
b = 3
c = -2

mencari nilai : x₁  +  x₂
x₁  +  x₂ = -b/a = - (3/-2) = 3/2
x_{1  .}  x₂ = c/a = (-2/-2) = 1

(x₁+ x₂)³ = (x₁  +  x₂)(x₁  +  x₂) (x₁  +  x₂)
(x₁+ x₂)³ = (x₁² + x₂² + 2x₁x₂)(x₁  +  x₂)
(x₁+ x₂)³ = x₁³ + x₁² x₂+ x₂² x₁ + x₂³ + 2x₁² x₂ + 2x₁x₂²
(x₁+ x₂)³ = x₁³ + x₂³+ 3 x₁² x₂+ 3 x₂² x₁
(3/2)³ = x₁³ + x₂³+ 3 x₁x₂ (x₁ + x₂)
27/8 = x₁³ + x₂³ +  3 . 1 (3/2)
27/8 - 9/2 = x₁³ + x₂^{3
x₁3 + x₂3} = 27/8 - 36/8
^{x₁3 + x₂3} = - 9/8

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