Se x³ = x + 2 ; x^10 = ?

 

Se x³ = x + 2 ; x^10 = ?

(x³)³ = (x + 2)³

Agora temos

x^9 = x³ + 3x²*2+3x*2^2 + 2³

x^9 = x³ + 6x²+12x + 8

x^9 = x + 2 + 6x²+12x + 8

x^9 = + 6x²+13x + 10

Mas queremos x^10

(x^9 = + 6x²+13x + 10)  x

x^10 = 6x³ + 13x² + 10 x

x^10 = 6(x + 2) + 13x² + 10 x

x^10 = 6x + 12 + 13x² + 10x

x^10 = 13x² + 10x + 6x + 12

x^10 = 13x² + 16x + 12

Jamal Malik