If \( (a-b),(b-c),(c-a) \) are in G.P., then prove that \( (a+b+c)^...

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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 (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)
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If a,b,c are in AP and x,y,z are in GP, then the value of x^(b-c).y^(c-a).z^(a-b) is...... If a,b,c are in AP and x,y,z are in GP, then the value of x^(b-c).y^(c-a).z^(a-b) is......
If `a ,b ,c` are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)` If `a ,b ,c` are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)`
If a, b, c are in G.P. then prove that: (a^2 + ab + b^2) / (bc + ca + ab) = (b + a) / (c + b) If a, b, c are in G.P. then prove that: (a^2 + ab + b^2) / (bc + ca + ab) = (b + a) / (c + b)
If a,b,c are in AP. Show thata(b+c)/bc, b(c+a)/ca, c(a+b)/ab are in AP | Arithmetic Progression If a,b,c are in AP. Show thata(b+c)/bc, b(c+a)/ca, c(a+b)/ab are in AP | Arithmetic Progression
Venn Diagrams (A intersection B, A Venn Diagrams (A intersection B, A' union B')