The cube root of `x+y+3x^(1/3)y^(1/3) (x^(1/3) + y^(1/3))` is

If x^2=y^3 , then prove that (x/y)^(3/2)+(y/x)^-(2/3)=x^(1/2)+y^(1/3) .

(1-x)^(3)-(1-y)^(3)+(x-y)^(3)

Evaluate : (x^(1//3)+y^(1//3))(x^(2//3)-x^(1//3)y^(1//3)+y^(2//3)) , when x=4(5)/(7) " and " y=5(2)/(7) .

If y=x^(1/3)-x^(-1/3) , prove that y^(3)+3y=x-(1)/(x)

If x^(3)=y^(4) prove that (x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)

If (x + y) ^((1)/(3)) + (y + x) ^((1)/(3)) =- ( z + x ) ^((1)/(3)) , then (x ^(3) + y ^(3) + z ^(3)) can be expressed as :

if y=3x+6x^(2)+10x^(3)+............ then the value of x in terms of y is (i) 1-(1-y)^(-(1)/(3))( ii) 1-(1+y)^((1)/(3))( iii) 1+(1+y)^(-(1)/(3))( iv )1-(1+y)^(-(1)/(3))