Answer:
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Step-by-step explanation:
Sol : - a,b,c = AP
A ( 1/b + 1/c ), b ( 1/c + 1/a ), c ( 1/a + 1/b ) = AP
b - a = c - b
b + b = a + c
2b = a + c
A ( 1/b + 1/c ) + c ( 1/a + 1/b ) = ( a/b + a/c ) + ( c/a + c/b)
= ( a+c/b ) + ( a/c + c/a )
= ( 2b/b ) + ( a² + c²/ ac )
= 2 + [ ( a + c )²/ac - 2 ]
= ( a + c )²/ac
= (a+c) (a+c)/ac
= 2b (a/ac + c/ac
A ( 1/b + 1/c ) + c ( 1/a + 1/b ) = 2b ( 1/c + 1/a )
A ( 1/b + 1/c ), b ( 1/c + 1/a ), c ( 1/a + 1/b ) = AP