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Show that (a-b)², (a²+b²), (a+b)² are in arithmetic progression.
Asked by apal63216 | 02 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 | 03 Jan, 2021, 11:27: AM

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