Answer:
1
Explanation:
Using the identity
a³ + b³ = (a + b)³ - 3ab(a + b), then
a³ + b³ + 3ab(a + b) = (a + b)³
a³ + b³ + 3ab(1) = 1³ , hence
a³ + b³ + 3ab = 1
Answer: 1
a + b = 1
a³ + b³ = (a + b)(a² - ab + b²) formula for a perfect cube
a³ + b³ + 3ab = (a + b)(a² - ab + b²) + 3ab
↓
= 1 (a² - ab + b²) + 3ab
= a² - ab + b² + 3ab
= a² + 2ab + b² this is a perfect square
= (a + b)(a + b)
↓ ↓
= (1) (1)
= 1
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