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(b+c)^(2)-a^(2),(c+a)^(2)-b^(2),(a+b)^(2...

(b+c)^(2)-a^(2),(c+a)^(2)-b^(2),(a+b)^(2)-c^(2)" are in "A.P

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If a,b,c are in A.P.prove that: (i) (1)/(bc),(1)/(ca),(1)/(ab) are in A.P.(ii) (b+c)^(2)-a^(2),(a+c)^(2)-b^(2),(b+a)^(2)-c^(2) are in A.P.

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

If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

If a, b, c are in A.P., prove that: (i) 1/(bc) , 1/(ca), 1/(ab) are in A.P. (ii) (b+c)^2- a^2 ,(a+c)^2- b^2 , (b+a)^2- c^2 are in A.P.

If (b^(2)+c^(2)-a^(2))/(2bc), (c^(2)+a^(2)-b^(2))/(2ca) and (a^(2)+b^(2)-c^(2))/(2ab) are in A.P. then show that, a(b+c-a), b(c+a-c) and c(a+b-c) are also in A.P. [a+b+c != 0] .

If (b^2+c^2-a^2)/(2b c),(c^2+a^2-b^2)/(2c a),(a^2+b^2-c^2)/(2a b) are in A.P. and a+b+c=0 then prove that a(b+c-a),b(c+a-b),c(a+b-c) are in A.P.

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

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

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