If `a ,b ,c ,d` are in G.P. prove that: `(a^2+b^2),(b^2+c^2),(c^2+d^2)` are in G.P. `(a^2-b^2),(b^2-c^2),(c^2-d^2)` are in G.P. `1/(a^2+b^2),1/(b^2+c^2),1/(c^2+d^2)` are in G.P. `(a^2+b^2+c^2),(a b+b c+c d),(b^2+c^2+d^2)`

Explanation

To prove the statements given in the question, we start by assuming that \( a, b, c, d \) are in geometric progression (G.P.). This means that there exists a common ratio \( r \) such that:

\[ b = ar, \quad c = ar^2, \quad d = ar^3 \]

### Step 1: Proving \( (a^2 + b^2), (b^2 + c^2), (c^2 + d^2) \) are in G.P.

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