Question

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Prove that (a - b)2, a2 + b2 and (a + b)2
three consecutive terms of an AP.​

Answer 1

a2 - a1 = ( a² + b² ) - ( a - b )²

= a² + b² - a² + 2ab - b²

= 2ab -----( 1 )

a3 - a2 =( a + b )² - ( a² + b² )

= a² + 2ab + b² - a² - b²

= 2ab ------( 2 )

From ( 1 ) and ( 2 ) ,

a2 - a1 = a3 - a1 = 2ab = common difference

Therefore ,

Above three terms are in A.P

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