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If a,b,c are in A.P., then prove that th...

If a,b,c are in A.P., then prove that the following are also in A.P
(i) `a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)` ltbr gt(ii) `1/(sqrtb+sqrtc),1/(sqrtc+sqrta),1/(sqrta+sqrtb)`
(iii) `a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)`

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To prove that the given sets of terms are in Arithmetic Progression (A.P.) when \( a, b, c \) are in A.P., we will analyze each part step by step. ### Part (i): Prove that \( a^2(b+c), b^2(c+a), c^2(a+b) \) are in A.P. 1. **Given**: \( a, b, c \) are in A.P. This means \( 2b = a + c \). 2. **To Prove**: The terms \( a^2(b+c), b^2(c+a), c^2(a+b) \) are in A.P. This means we need to show: \[ ...
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