Show that (a-b)², (a²+b²), (a+b)² are in arithmetic progression.

Asked by apal63216 | 2nd Jan, 2021, 07:40: PM

Expert Answer:

Hint
Check if the common difference is same. If so, the given progression will be AP.
 
(a - b)², (a² + b²), (a + b)²
 
1st term = (a - b)²
2nd term = (a² + b²)
3rd term = (a + b)²
 
Check 2nd term - 1st term
= (a² + b²) - (a - b)²
= (a² + b²) - (a2 - 2b + b2)
= 2b
 
Check 3rd term - 2nd term
= (a + b)² - (a² + b²)
= a2 + 2b + b2 - a² - b²
= 2b
 
So the common difference is same. Its is AP.
 

Answered by  | 3rd Jan, 2021, 11:27: AM