Question

if x+y=12 and xy=27, find the value of x³+y³​

Answer 1

Answer:

x^3+y^3=(x +y)(x^2-xy+y^2)

putting the value we get

=12 (x^2-27+y^2)

=12 (x^2+y^2-27) (1)

(x+y)^2=x^2+y^2+2xy

x^2+y^2=(x+y)^2-2xy

putting the values in (1)

=12( (x+y)^2-2xy-27)

12 (12×12-2×27-27)

12 (144-54-27)

12 (144-81)

12× 63=756 Answer

Answer 2

Answer:

We know that

(x + y)³ = x³ + y³ + 3xy(x + y)

Putting x + y = 12 and xy = 27 in the

above identity, we get

12³ = x³ + y³ + 3 × 27 × 12

=> 1728 = x³ + y³ + 972

=> x³ + y³ = 1728 - 972

=> x³ + y³ = 726.

Hence, the value of x³ + y³ is 726.