If `a^2(b+c),b^2(c+a),c^2(a+b),` are in A.P. show that either `a ,b ,c` are in A.P., or `a b+b c+c a=0.`

Similar Questions

Explore conceptually related problems

If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b, c are in A.P. or ab + bc + ca =0.

If a^(2)(b+c),b^(2)(c+a),c^(2)(a+b) are in A.P. then prove that a,b,c are in A.P.or ab+bc+ca=0

If (b+c),(c+a),(a+b) are in H.P. show that a^2 ,b^2 , c^2 are in A.P.

If a^(2),b^(2),c^(2) are in A.P. ,then show that b+c,c+a,a+b are in H.P.

If a^(2),b^(2),c^(2) are in A.P,then show that: b+c-a,c+a-b,a+b-c are in A.P.

If a^(2), b^(2), c^(2) are in A.P., show that, (b+c), (c+a), (a+b) are in H.P.

If a,b,c are in G.P., show that 1/(a+b),1/(2b),1/(b+c) are in A.P.

If a^(2),b^(2),c^(2) are in A.P,show that: (a)/(b+c),(b)/(c+a),(c)/(a+b) are in A.P.

If (b-c)^2,(c-a)^2,(a-b)^2 are in A.P. show that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.

If (b+c)/a,(c+a)/b,(a+b)/c are in A.P. show that 1/a,1/b1/c are also in A.P. (a +b+c != 0) .