If `(a+1/b) = (b+1/c) =(c+1/a)` then find `a^2b^2c^2`

If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(b-1)^2,(c-1)^2)|= then

The area of triangle formed by the vertices (a, 1/a), (b, 1/b), (c, 1/c) is (a) |((a+b)(b+c)(c+a))/(2abc)| (b) |((a-b)(b-c)(c-a))/(2abc)| (c) |((a-(1)/(a))(b-(1)/(b))(c-(1)/(c )))/(2)| (d) |((a-1)(b-1)(c-1))/(2abc)|

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

If |(a^2,b^2,c^2),((a+1)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

If a ,b ,c are in A.P., prove that the following are also in A.P. (i) 1/(b c),1/(c a),1/(a b), (ii) b+c ,c+a ,a+b (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) (iv) a^2(b+c),b^2(c+a),c^2(a+b) (v) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

A plane makes intercepts O A ,O Ba n dO C whose measurements are a,b and c on the O X ,O Ya n dO Z axes. The area of triangle A B C is a. 1/2(a b+b c+c a) b. 1/2a b c(a+b+c) c. 1/2(a^2b^2+b^2c^2+c^2a^2)^(1//2) d. 1/2(a+b+c)^2

If (2)/(b)=(1)/(a)+(1)/(c) ,then the value of (log(a+c)+log(a-2b+c))/(log(a-c)) is

If a, b , c are in GP, then 1/(a^(2 )−b^2 )+1/b^2 = ?

The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c, k^2+c^2, 1)| is (A) k(a+b)(b+c)(c+a) (B) k a b c(a^2+b^(2)+c^2) (C) k(a-b)(b-c)(c-a) (D) k(a+b-c)(b+c-a)(c+a-b)

Prove: |(a^2+1,a b ,a c), (a b,b^2+1,b c), (c a,cb,c^2+1)|=1+a^2+b^2+c^2