c=1,a^(2)+b^(2)+c^(2)=9,a^(3)+b^(3)+c^(3)=1" then "(1)/(a)+(1)/(b)

If a+b+c=1,a^(2)+b^(2)+c^(2)=9 and a^(3)+b^(3)+c^(3)=1, then (1)/(a)+(1)/(b)+(1)/(c) is (i)0 (ii) -1(iii)1(iv)3

|(1,1,1),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3))|=

If a+b+c=1 , a^2+b^2+c^2=9 and a^3+b^3+c^3=1 , then 1/a + 1/b + 1/c is (i) 0 (ii) -1 (iii) 1 (iv) 3

If a+b+c=1 , a^2+b^2+c^2=9 and a^3+b^3+c^3=1 , then 1/a + 1/b + 1/c is (i) 0 (ii) -1 (iii) 1 (iv) 3

If |[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|=5, then the value of |[b_(2)c_(3)-b_(3)c_(2),a_(3)c_(2)-a_(2)c_(3),a_(2)b_(3)-a_(3)b_(2)],[b_(3)c_(1)-b_(1)c_(3),a_(1)c_(3)-a_(3)c_(1),a_(3)b_(1)-a_(1)b_(3)],[b_(1)c_(2)-b_(2)c_(1),a_(2)c_(1)-a_(1)c_(2),a_(1)b_(2)-a_(2)b_(1)]| is

By using properties of determinants , show that : (i) {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) (ii) {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c)