Question

If a+b=3 and ab=4 find the value of a3+b3

Answer 1

Answer:

63

Step-by-step explanation:

Expand the formula (a - b)²:

(a - b)² = a² - 2ab + b²

Rearrange it to make a² + b² the subject:

a² + b² = (a - b)² + 2ab

Expand a³ - b³:

a³ – b³ = (a – b)(a² + b² + ab )

sub a² + b² = (a - b)² + 2ab:

a³ – b³ = (a – b)((a - b)² + 2ab + ab )

a³ – b³ = (a – b)((a - b)² + 3ab)

Sub a - b = 3 and ab = 4:

a³ – b³ = (3)((3)² + 3(4))

a³ – b³ = (3)(9 + 12)

a³ – b³ = (3)(21)

a³ – b³ = 63