`((1)/(3)a+(2)/(3)b)^(3)-((1)/(3)a-(2)/(3)b)^(3)`

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)

(a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/a)^(3)+.... =

(a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/a)^(3)+.... =

Find the values of a and b, when: (i) (a+3,b-2)=(5,1) (ii) (a+b,2b-3)=(4,-5) (iii) ((a)/(3)+1,b-(1)/(3))=((5)/(3),(2)/(3)) (iv) (a-2,2b+1)=(b-1,a+2)

If the line segment joining the points (3,-4), and (1,2) is trisected at points P(a,-2) and Q((5)/(3),b). Then,a=(8)/(3),b=(2)/(3) (b) a=(7)/(3),b=0a=(1)/(3),b=1(d)a=(2)/(3),b=(1)/(3)

If a, b, c are in G.P., show that a^(2)b^(2)c^(2)((1)/(a^(3))+(1)/(b^(3))+(1)/(c^(3))) = a^(3) + b^(3) + c^(3) .

Multiply (a^(3) b^(2))/(a-1) " by " (a^(2)-1)/(a^(2)b^(3))

If a=3^((1)/(4))+3^(-(1)/(4)) and b=3^((1)/(4))-3^(-(1)/(4)) then the value of 3(a^(2)+b^(2))^(2)