Question

Se x-y=2 e x^2 + y^2 =8, determine o resultado para x^3 - y^3

Answer 1

Resposta:

(x-y)²=x²+2*xy+y²

2² =x²+y²+2xy

4 =8+2xy

xy=-2

(x-y)³=x³-3x²y+3xy²-y³

2³ =x³-y³ -3xy(x-y)

2³ =x³-y³ -3*(-2) * (-2)

8 =x³-y³-12

x³-y³ =8+12

x³-y³ =20