Pertanyaan

[ Simulasi UN 2015 ] Persamaan kuadrat − 2 x 2 + 3 x − 2 = 0 memiliki akar − akar a dan b maka nilai a 3 + b 3 = ⋯

$[Simulasi UN 2015] Persamaan kuadrat - 2 x^{2} + 3 x - 2 = 0 memiliki akar - akar a dan b maka nilai a^{3} + b^{3} = \dots$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$D a r i space p e r s a m a a n space k u a d r a t space d i k e t a h u i space space a plus b equals fraction numerator left parenthesis negative 3 right parenthesis over denominator left parenthesis negative 2 right parenthesis end fraction equals 3 divided by 2 space a. b equals fraction numerator left parenthesis negative 2 right parenthesis over denominator left parenthesis negative 2 right parenthesis end fraction equals 1$

$space a cubed plus b cubed equals left parenthesis a plus b right parenthesis cubed minus 3 a b left parenthesis a plus b right parenthesis space S e h i n g g a space d a p a t space d i s u b s t i t u s i k a n space n i l a i space left parenthesis a plus b right parenthesis space d a n space left parenthesis a. b right parenthesis space a cubed plus b cubed equals left parenthesis 3 over 2 right parenthesis cubed minus 3 left parenthesis 1 right parenthesis left parenthesis 3 over 2 right parenthesis space space space space space space space space space space space space equals 27 over 8 minus 9 over 2 equals fraction numerator left parenthesis 27 minus 36 right parenthesis over denominator 8 end fraction space space space space space space space space space space space space equals negative 9 over 8$