Question

if x+y=12 and xy = 27 find the value of x^3 + y^3 .

Answer 1

X + Y = 12
Cubing both sides.
X^3 + Y^3 + 3xy(x+y) = 1728
x + y = 12
XY = 27
X^3 + Y^3 + 3*12*27 = 1728
X^3 + Y^3 = 1728 - 3*12*27
=1728 - 972
=756

Answer 2

EXPLANATION.

⇒ x + y = 12. - - - - - (1).

⇒ xy = 27. - - - - - (2).

As we know that,

Formula of :

⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³.

Using this formula in this question, we get.

Cubing on both sides of the equation (1), we get.

⇒ (x + y)³ = (12)³.

⇒ x³ + 3x²y + 3xy² + y³ = 1728.

⇒ x³ + y³ + 3x²y + 3xy² = 1728.

⇒ x³ + y³ + 3xy(x + y) = 1728.

Put the value of equation (2) in this expression, we get.

⇒ x³ + y³ + 3(27)(12) = 1728.

⇒ x³ + y³ + 972 = 1728.

⇒ x³ + y³ = 1728 - 972.

⇒ x³ + y³ = 756.

∴ The value of x³ + y³ is 756.