`text(Ta có :)`
`a^5 + b^5 = (a^3 + b^3)(a^2 + b^2) - (a + b)`
`⇔ a^5 + b^5 = a^5 + a^3b^2 + b^3a^2 + b^5 - (a + b)`
`⇔ a^5 + b^5 = a^5 + b^5 + a^2b^2(a + b) - (a + b)`
`⇔ a^5 + b^5 = a^5 + b^5 + (a + b)(a^2b^2 - 1)`
`Do ab = 1`
`⇔ a^5 + b^5 = a^5 + b^5 + (a + b)(a^2b^2 - 1)`
`⇔ a^5 + b^5 = a^5 + b^5 + (a + b) . 0`
`⇒ a^5 + b^5 = a^5 + b^5 (đpcm)`
`Vậy ab = 1 thì a^5 + b^5 = (a^3 + b^3)(a^2 + b^2) - (a + b)`