Question

If a+b=12 and ab=27 then the value of a³+b³​

Answer 1

Answer:

756

Step-by-step explanation:

a³+b³​ = (a+b)³ - 3ab(a+b)

given a+b=12; ab=27, we have

a³+b³​ =12³ - 3(27)(12)

         = 12(12²-3(27))

         = 12(144-81)

         = 12(63)

         = 756

Answer 2

Given :-

• a + b = 12
• ab = 27

To find :-

• a³ + b³

Solution :-

• a + b = 12
• ab = 27

Cube both side

→ (a + b)³ = (12)³

• Apply identity
• (a + b)³ = a³ + b³ + 3ab(a + b)

→ a³ + b³ + 3ab(a + b) = 1728

• Put the values

→ a³ + b³ + 3 × 27 × 12 = 1728

→ a³ + b³ + 972 = 1728

→ a³ + b³ = 1728 - 972

→ a³ + b³ = 756

Hence,

• The value of a³ + b³ is 756

More to know :-

• (a - b)² = a² + b² - 2ab

• (a + b)² = a² + b² + 2ab

• a² - b² = (a + b)(a - b)