Question

if x/y +y/x=1, then value of xcube +y cube is : options are a. 0 b.1 c.x+y d.-1

Answer 1

Given x/y + y/x = 1

= > (x^2 + y^2) = 1 * xy

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

= > x^2 + y^2 - xy = 0

We know that a^3 + b^3 = (a + b)(a^2 + b^2 - ab)

Now,

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

                = (x + y)(0)

                = 0.


Therefore the answer is the option (a) - 0.


Hope this helps!

Answer 2

x/y + y/x = 1    {Given } 


(x^2 + y^2)/xy = 1 

x^2 + y^2 = xy 


Adding 2xy on both sides,


x^2 + y^2 + 2xy = xy + 2xy 


(x + y)^2 = 3xy 

(x + y) = √3xy 



Cube on both sides,


(x + y)^3 = (√3xy)^3 


x^3 + y^3 + 3xy(x + y) = 3xy√3xy


x^3 + y^3 + 3xy(√3xy) = 3xy√3xy 


x^3 + y^3 + 3xy√3xy = 3xy√3xy 


x^3 + y^3 = 3xy√3xy  - 3xy√3xy 


x^3 + y^3 = 0 



Option (a) is correct.