Question

If x+y=12 and xy=27,then find thevalue of x^3+y^3

Answer 1

By using the identity,

a³ + b³ = (a + b)(a² + b² - ab)

Here, x = a and b = y

x + y = 12 given
xy = 27 given

x² + y² = ??

Using the identity,
a² + b² = (a + b)² - 2ab
we get

x² + y² = (x + y)² - 2xy

=> (12)² - 2(27)

=> x² + y² = 144 - 54

=> x² + y² = 90

Now substituting the value we get,

x³ + y³ = (x + y)(x² + y² - xy)

=> x³ + y³ = (12)(90 - 27)

=> x³ + y³ = (12)(63)

=> x³ + y³ = 756

Your answer $\boxed{756}$

Hope it helps dear friend ☺️✌️