यदि a, b , c A.P. में हैं , तो सिद्ध करें कि
`(b + c)^(2) - a^(2) , (c + a)^(2) - b^(2) , ( a + b)^(2) - c^(2)` A.P. में हैं ।

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 (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.

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

If a, b, c are in A.P. then show that the terms given below are also in A.P. (b+c)^2-a^2,(c+a)^2-b^2,(a+b)^2-c^2 .

If In (a + c), In(c - a) , In(a - 2b + c) are in A.P., then

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