If A is the A.M between a and b prove that :
(i) `(A-a)^(2)+(A-b)^(2)=1/2(a-b)^(2)`
(ii) `4(a-A)(A-b)=(a-b)^(2)`

If A is the A.M.between a and b, prove that (A+2a)/(A-b)+(A+2b)/(A-a)=4

If A_(1) and A_(2) are two A.M.'s between a and b, prove that (i) (2A_(1)-A_(2))(2A_(2)-A_(1))=ab (ii) A_(1)+A_(2)=a+b

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).

In any DeltaABC , prove that (cos2A)/a^(2)-(cos2B)/b^(2)=(1/a^(2)-1/b^(2))

Some Important Identities - (i) (a+b)^(2)=a62+2ab+b^(2)( ii) (a-b)^(2)=a^(2)-2ab+b^(2)

Find the AM between (i) 13 and 19 (ii) (a-b) and (a+b)

If a,b, and c are in G.P.then prove that (1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))

If a+b=1, and a,b>0, then prove that (a+(1)/(a))^(2)+(b+(1)/(b))^(2)>=(25)/(2)

If a, b, c are in G.P., x and y are the A.M.'s of a, b and b, c respectively, then prove that: (i)(a)/(x)+(c)/(y)=2" "(ii) (1)/(y)+(1)/(y)=(2)/(b)