akar akar persamaan kuadrat x2 - (m+2) x +2m=0 adalah x1 dn x2. jika x1^3 + x2^3 =16 nilai m E R yang memenuhi axalah

jawab

x^2 -(m+2)x + 2m =0
x1+ x2 = m + 2
x1 . x2 = 2m

x1^3 + x2^3 = 16
(x1+ x2)^3 - 3 x1x2 (x1 +x2) = 16
(m+2)³ - 3(2m)(m+2) = 16
(m+2)³ - 6m² - 12m - 16=0
m² + 6m²+ 12m + 8 - 6m² -12m - 16 = 0
m³ - 8 = 0
m³ = 8
m = 2