If ` x = a^(1/3) b^(-1/3) + a^(-1/3) b^(1/3)` then prove that ` a(bx^(3) - 3bx -a) = b^(2)`

If x = a^((1)/(3)) b^((1)/(3)) + a^(-(1)/(3)) + a^(-(1)/(3)) b^((1)/(3)) then prove that a(bx^(3) - 3bx - a) = b^(2)

If a+b=1 then prove that a^3+b^3+3ab=1

If x = (a + sqrt(a^(2) + b^(3)))^((1)/(3)) + (a-sqrt(a^(2) + b^(3)))^((1)/(3)) , then what is the value of x^(3) + 3bx - 2a ?

If x=(a+sqrt(a^2+b^3))^(1//3)+(a-sqrt(a^2+b^3))^(1//3) then what x^3+3bx-2a

If (a+bx)^(-3) = (1)/(27) + (1)/(3) x + ….. then the ordered pair (a, b)=

if x = (sqrt(3a + 2b) + sqrt(3a - 2b))/(sqrt(3a + 2b) - sqrt(3a - 2b)) prove that : bx^(2) - 3ax + b = 0

If x = (sqrt(a + 3b) + sqrt(a - 3b))/ (sqrt(a + 3b) - sqrt(a - 3b)) prove that : 3bx^(2) - 2ax + 3b = 0 .

If lim_(x to 1) (1 + ax + bx^(2))^((c )/(x - 1)) = e^(3) , then the value of a + b + bc + 2009 is…….

If lim_(x to 1) (1 + ax + bx^(2))^((c )/(x - 1)) = e^(3) , then the value of a + b + bc + 2009 is…….

If ax^((2)/(3))+bx^((1)/(3))+c-0 then the value of a^(3)x^(2)+b^(3)x+ cis given by