`(a(a+c-b))/(b(b+c-a))i s`

if R=-S=T=-(a+b+c)(a-b)(b-c)(c-a) Proof R= a^3(b-c)+b^3(c-a)+c^3(a-b)

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a , ba n dc are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

S.T |(1,a,a^2),(1,b,b^2),(1,c,c^2)| = (a-b)(b-c)(c-a) .

If a,b,c are the sides of triangle then (a)/(c +a -b) + (b)/(a +b -c) + (c )/(b +c-a) can take vlaue (s)

If 1/a,1/b,1/c are in AP, prove that (i) ((b+c))/a, ((c+a))/b,((a+b))/c are in AP. (ii) ((b+c-a))/a,((c +a-b))/b, ((a+b-c))/c are in AP .

If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in A.P, prove that 1/a,1/b,1/c are also A.P.s