Question

if x+y=12 and xy=27,find value of x^3+y^3​

Answer 1

Given that, x+y=12 and xy=27

We know,

(x+y)3=x3+y3+3xy(x+y)

Therefore,

123=x3+y3+3×27×12

1728=x3+y3+972

x3+y3=1728−972=756

∴x3+y3=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.