Show that (a–b) 2 , (a 2 +b 2 ) and (a + b) 2 are in A.P.

Question

Show that (a&#x2013;b) 2 , (a 2 +b 2 ) and (a + b) 2 are in A.P.

Philoid · Accepted Answer

The terms given below are : (a–b)², (a²+b²) and (a + b)²

Common difference, d₁ = a² + b² – (a – b)²

d₁= a² + b² – (a² + b² - 2ab)

d₁= a² + b² – a² - b² + 2ab

d₁= 2ab

Common difference, d₂ = (a + b)² – (a² + b²)

d₂ = a² + b² + 2ab – a² –b²

d₂ = 2ab

Since, d₁ = d₂i.e. the common difference is same.

Therefore, the given terms are in A.P.