ab^(2)+(a-1)b-1

If 5a-b, 2a+b, a+2b are in A.P. and (a-1)^(2), (ab+1),(b+1)^(2) are in G.P., a ne 0 , then a is equal to

Find the sum of n terms of the series ab+(a-1)(b-1)+(a-2)(b-2)+.... if ab=1/6 and a+b=1/3 .

Find the value of 2a^(4)xx(-(1)/(8)ab^(2))xx(16ab^(2)c) when a=-1;b=1;c=-1

det[[1,x,x^(2)1,y,y^(2)1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2b1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2bc^(2),1,2c]]=det[[(a-x)^(2),(b-x^(2)),(c-x)^(2)(a-y)^(2),(b-y)^(2),(c-y)^(2)(a-z)^(2),(b-z)^(2),(c-z)^(2)]]

If [ sqrt (a ^(2) + b^(2) + ab)] + [ sqrt (a^(2) + b^(2) - ab)] = 1 then what is the value of (1 - a^(2)) (1 - b^(2)) ?

If a+ b = 4 and ab =3 , find (1)/(b^(2)) + (1)/(a^(2))

Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

The value of the determinant |{:(1+ a^(2) - b^(2),2 ab , - 2b),(2ab, 1 - a^(2) + b^(2), 2a),(2b , -2a , 1-a^(2) - b^(2)):}| is equal to

If A=[[1,-12,3]] and B=[[2,3-1,-2]], then which of the following is/are correct? 1.AB(A^(-1)B^(-1)) is a unit matrix.2.(AB)^(-1)=A^(-1)B^(-1)

If sintheta+costheta=a and (sintheta+costheta)/(sinthetacostheta)=b , then (a) b=(2a)/(a^2-1) (b) a=(2b)/(b^2-1) (c) ab=b^2-1 (d) a+b=1