Cho: a+b=5; ab=-2
a² + b²
= a² + 2ab + b² - 2ab (hằng đẳng thức thứ 1)
= (a + b)² - 2ab
= 5² - 2(-2) = 5² + 4 = 25 + 4 = 29
$\frac{1}{a^{3}}$ + $\frac{1}{b^{3}}$
= $(\frac{1}{a})^{3}$ + $(\frac{1}{b})^{3}$
= ($\frac{1}{a}$ + $\frac{1}{b}$) - 3$(\frac{1}{a})^{2}$ $\frac{1}{b}$ - 3$\frac{1}{a}$$(\frac{1}{b})^{2}$
= ($\frac{1}{a}$ + $\frac{1}{b}$) - 3$\frac{1}{a}$$\frac{1}{b}$($\frac{1}{a}$ - $\frac{1}{b}$)
= ($\frac{1}{a}$ + $\frac{1}{b}$) + $\frac{3}{2}$($\frac{1}{a}$ - $\frac{1}{b}$)
= chưa nghĩ ra
a - b
= - (a + b)
= - 5
a³ - b³
= (a - b) (a² + ab + b²)
= (a - b) (a² - 2 + b²)
= (a - b) (a² + b² - 2)
=(a - b) (29 - 2) = (a - b) 27
= - (a + b)27
= -5 . 27
= -135
