((1)/(3)a+(2)/(3)b)((1)/(3)a+(2)/(3)b)

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

It is given that the events A and B are such that P(A)=(1)/(4),P((A)/(B))=(1)/(2) and p((B)/(A))=(2)/(3) Then P(B) is: (1)(1)/(6)(2)(1)/(3)(3)(2)/(3)(4)(1)/(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)+.... =

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

det[[2a_(1)b_(1),a_(1)b_(2)+a_(2)b_(1),a_(1)b_(3)+a_(3)b_(1)a_(1)b_(2)+a_(2)b_(1),2a_(2)b_(2),a_(2)b_(3)+a_(3)b_(2)a_(1)b_(3)+a_(3)b_(1),a_(3)b_(2)+a_(2)b_(3),2a_(3)b_(3)]]=