If a,b,c are unequal numbers in A.P. such that a,b-c,c-a are in G.P. then

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If a,b,c are three unequal numbers such that a,b,c are in A.P and b−a,c−b,a are in G.P, then a:b:c If a,b,c are three unequal numbers such that a,b,c are in A.P and b−a,c−b,a are in G.P, then a:b:c
If (a - b) (b - c) (ca) are in G.P., then prove that (a + b + c) ^ 2 = 3(ab + bc + ca) If (a - b) (b - c) (ca) are in G.P., then prove that (a + b + c) ^ 2 = 3(ab + bc + ca)
If (a-b),(b-c),(c-a) are in GP then prove that (a+b+c)^2=3(a b+b c+c a). If (a-b),(b-c),(c-a) are in GP then prove that (a+b+c)^2=3(a b+b c+c a).
If three unequal positive real numbers a, b, c are in G.P. and b-c, c-a, a - b are in H.P,then t... If three unequal positive real numbers a, b, c are in G.P. and b-c, c-a, a - b are in H.P,then t...
If \( (a-b),(b-c),(c-a) \) are in G.P., then prove that \( (a+b+c)^... If \( (a-b),(b-c),(c-a) \) are in G.P., then prove that \( (a+b+c)^...
If a,b,c are three unequal numbers such that a,b,c are in A.P. and (b-a) ,. (c-b) ,a are in G.P... If a,b,c are three unequal numbers such that a,b,c are in A.P. and (b-a) ,. (c-b) ,a are in G.P...
If \( a, b, c \) are in G.P. and \( a-b, c-a \) and \( b-c \) are in H.P., then \( a+4 b+c \) is... If \( a, b, c \) are in G.P. and \( a-b, c-a \) and \( b-c \) are in H.P., then \( a+4 b+c \) is...
If three unequal positive numbers a, b, c are in G.P. then show that, `a +c gt 2b`. If three unequal positive numbers a, b, c are in G.P. then show that, `a +c gt 2b`.