(a + b)³ = a³ + b³ + 3a²b + 3ab²

(a + b)³ = a³ + b³ + 3ab(a + b)

jawab :

∛x + ∛(x - 16) = ∛(x - 8)

kubikkan kedua ruas..

(∛x + ∛(x - 16))³ = (∛(x - 8))³

x + (x - 16) + 3(∛x)(∛(x - 16)(∛(x - 8)) = x - 8

2x - 16 + 3(∛x)(∛(x - 16)(∛(x - 8)) = x - 8

3(∛x)(∛(x - 16)(∛(x - 8)) = -x + 8

kubikkan kedua ruas lagi..

(3(∛x)(∛(x - 16)(∛(x - 8)))³ = (-x + 8)³

27x (x - 16) (x - 8) = -(x - 8)³

27x (x - 16) (x - 8) + (x - 8)³ = 0

27x (x - 16) (x - 8) + (x - 8) (x - 8) (x - 8) = 0

faktorkan..

(x - 8) (27x(x - 16) + (x - 8)²) = 0

solusi pertama :

x - 8 = 0

x1 = 8

27x(x - 16) + (x - 8)² = 0

27x² - 432x + x² - 16x + 64 = 0

28x² - 448x + 64 = 0

7x² - 112x + 16 = 0

rumus kuadratik :

x = -b +- √b² - 4ac / 2a

x = 112 +- √-112² - 4(7)(16) / 2(7)

x = 112 +- √12544 - 448 / 14

x = 112 +- √12096 / 14

x = 112 +- 24√21 / 14

x = 8 +- 12√21 / 7

solusi kedua :

x2 = 8 + 12√21 / 7

solusi ketiga :

x3 = 8 - 12√21 / 7

maka, nilai x adalah..

x1 = 8

x2 = 8 + 12√21 / 7

x3 = 8 - 12√21 / 7