Show that `(b-c)/(r _(1))+ (c-a)/(r _(2))+(c-a)/(r _(3)) =0.`

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

Sum of the first p,q and r terms of an A.P. are a, b and c, respectively. Prove that, (a)/(p) (q-r) + (b)/(q) (r-p) + (c )/(r ) (p-q) = 0

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

If x=a + (a)/(r ) + (a)/(r^(2)) + …..oo, y= b - (b)/(r ) + (b)/(r^(2))-……..oo and z= c + (c )/(r^(2)) + (c )/(r^(4))+ ….oo then prove that (xy)/(z)= (ab)/(c )

Show that (d)/(dx) e^(ax) cos (bx + c) = r e^(ax) cos (bx + c + alpha) where r= sqrt(a^(2) + b^(2)), cosalpha= (a)/(r ), sin alpha = (b)/(r ) and (d^(2))/(dx^(2)) e^(ax) cos (ax + c) = r^(2) e^(ax ) cos (bx + c + 2 alpha) .

Let R be a relation on N xx N defined by (a,b) R(c, d) hArr a + d= b + c for all (a,b) (c,d) in N xx N show that, (a,b) R (c, d) rArr (c, d) R (a, b) for all (a, b) (c, d) in N xx N

If a,b,c are respectively the p^(th), q^(th) and r^(th) terms of the given G.P. then show that (q - r) log a + (r - p) logb + (p - q) log c = 0, where a, b, c gt 0

Statement -1 Consider the determinant Delta=|{:(a_(1)+b_(1)x^(2),a_(1)x^(2)+b_(1),c_(1)),(a_(2)+b_(2)x^(2),a_(2)x^(2)+b_(2),c_(2)),(a_(3)+b_(3)x^(2),a_(3)x^(2)+b_(3),c_(3)):}|=0, where a_(i),b_(i),c_(i) in R (i=1,2,3) and x in R Stement -2 If |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| =0, then Delta =0

A : Three capacitors having C_(1) lt C_(2) lt C_(3) are connected in parallel its effective capacitance will be C_(p) gt C_(3) . R : (1)/(C_(P))=(1)/(C_(1))+(1)/(C_(2))+(1)/(C_(3))

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z} . Show that (i) (a,a) in R" for all " a in Q (ii) (a,b) in R implies that (b,a) inR (iii) (a,b) in R and (b,c) in R implies that (a,c) in R