If `(a" "+" "i b)" "(c" "+" "i d)" "(e" "+" "if)" "(g" "+" "i h)" "=" "A" "+" "i B` , then show that `(a^2+b^2)(c^2+d^2)(e^2+f^2)(g^2+h^2)=A^2+B^2`

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2) = (ab+bc+cd)^2

If A = {b, c, e, g, h}, B = {a, c, d, g, i} and C = {a, d, e, g, h}, then show that A-(BcapC)=(A-B)cup(A-C) .

If a,b,c and the d are in H.P then find the vlaue of (a^(-2)-d^(-2))/(b^(-2)-c^(-2))

If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

If a,b,c,d are in geometric sequence then prove that (b-c)^(2) +(c-a)^(2) -(d-b)^(2)=(a-d)^2

If A=((a, b), (c, d)) and I=((1, 0), (0, 1)) show that A^(2)-(a+d)A=(bc-ad)I_(2).

If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=xdot If the curve passes through (1,0), then the curve is (a) ( b ) (c)2y=( d ) x^(( e )2( f ))( g )-x (h) (i) (b) ( j ) (k) y=( l ) x^(( m )2( n ))( o )-x (p) (q) (c) ( d ) (e) y=x-( f ) x^(( g )2( h ))( i ) (j) (k) (d) ( l ) (m) y=2(( n ) (o) x-( p ) x^(( q )2( r ))( s ) (t))( u ) (v)

If f(x)=|x+a^2 a b ac a b x+b^2 bc a c b c x+c^2|, t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot