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geniusboy [140]
3 years ago
12

If a+b=1, find N=a^3+b^3+3ab

Mathematics
2 answers:
mart [117]3 years ago
4 0

Answer: 1

<u>Step-by-step explanation:</u>

a + b = 1

a³ + b³ = (a + b)(a² - ab + b²)         <em>formula for a perfect cube</em>

a³ + b³ + 3ab = (a + b)(a² - ab + b²) + 3ab

                            ↓

                     =     1     (a² - ab + b²) + 3ab

                     =           a² - ab + b² + 3ab

                     =           a² + 2ab + b²         <em>this is a perfect square</em>

                     =           (a + b)(a + b)

                                      ↓       ↓

                     =              (1)      (1)

                     =                   1

avanturin [10]3 years ago
4 0

Answer:

1

Step-by-step 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

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