x=a^((1)/(3))b^(-(1)/(3))+a^(-(1)/(3))b^((1)/(3))" 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 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 + 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 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 x^3+3bx-2a

int_(0)^(1)(acx^(b+1)+a^(3)bx^(3b+5))dx

The value of the determinant Delta = |((1 - a_(1)^(3) b_(1)^(3))/(1 - a_(1) b_(1)),(1 - a_(1)^(3) b_(2)^(3))/(1 - a_(1) b_(2)),(1 - a_(1)^(3) b_(3)^(3))/(1 - a_(1) b_(3))),((1 - a_(2)^(3) b_(1)^(3))/(1 - a_(2) b_(1)),(1 - a_(2)^(3) b_(2)^(3))/(1 - a_(2) b_(2)),(1 - a_(2)^(3) b_(3)^(3))/(1 - a_(2) b_(3))),((1 - a_(3)^(3) b_(1)^(3))/(1 - a_(3) b_(1)),(1 - a_(3)^(3) b_(2)^(3))/(1 - a_(3) b_(2)),(1 - a_(3)^(3) b_(3)^(3))/(1 - a_(3) b_(3)))| , is

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

Resolve into Partial Fractions If (1)/(x^(3)(x+3))=(1)/(Ax) - (1)/(Bx^(2))+(1)/(Cx^(3))-(1)/(D(x+3)) then find the values of A, B, C and D.