Question

cho a+b=6

a^2+b^2=201

tính: M=a^3+b^3

Answer 1

Ta có: a + b = 6 => (a + b)² = 36 => a² + b² + 2ab = 36 

  mà a² + b² = 201 => 201 + 2ab = 36 => 2ab = -165 => ab = -165/2

M = a³ + b³ = (a + b)(a² - ab + b²) = 6.(201 + 165/2) = 1701

                                     Vậy M = 1701

Answer 2

\(a+b=6\Rightarrow\left(a+b\right)^2=36\Rightarrow a^2+2ab+b^2=36\Rightarrow2ab=36-201=-165\Rightarrow ab=-\frac{165}{2}\)

Mặt khác: \(\left(a+b\right)\left(a^2+b^2\right)=a^3+b^3+ab\left(a+b\right)=6\cdot201=1206\)

\(\Rightarrow a^3+b^3=1206-\left(-\frac{165}{2}\right)\cdot6=1701\).