Question

if a,b,c are in AP .than prove that (a-c)² = 4(b²-ac)

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Answer 1

Answer:

Step-by-step explanation:

Since a, b, c are in A.P so

                      b – a = c – b

                     b + b = c + a

                        2 b = c + a

 Taking squares on both sides

                     (2 b) ² = (c + a)²

                     4b² = (c + a)²

Subtracting by 4ac on both sides, we get

               4b² – 4ac  = (c + a)² – 4 ac

               4(b² – ac)  = c² + a² + 2 ac – 4 ac

               4(b² – ac)  = c² + a² - 2 ac

               4(b² – ac)  = ( a-c )²