Question

If x+y=12 & xy=27 find x^3+y^3

Answer 1

Step-by-step explanation:

let us remember (a+b)^3 formula

i.e a^3+b^3+3ab(a+b)

now from problem we have

x+y=12

xy=27

now replace values in

(x+y)^3=x^3+y^3+3xy(x+y)

(12)^3=x^3+y^3+3(27)(12)

1728=x^3+y^3+972

x^3+y^3=1728-972

=756

therefore x^3+y^3=756

Answer 2

Answer:

→ x + y = 12

Cube on both sides

→ ( x + y )³ = 12³

Using ( a + b )³ = a³ + b³ + 3ab( a + b )

→ x³ + y³ + 3xy( x + y ) = 1728

Given xy = 27

→ x³ + y³ + 3(27)(12) = 1728

→ x³ + y³ + 972 = 1728

→ x³ + y³ = 1728 - 972

→ x³ + y³ = 756

Hence the required value is 756