Question

Find the value of (a-b), given that a2+b2 = 970 and ab = 483.​

Answer 1

( a - b)² = a² + b² - 2ab

( a - b)² = 970 - 2*483 = 970 - 966 = 4

( a - b) = √ 4 = +- 2 Ans.

Answer 2

Before we solve this problem, we must get well acquainted with some algebraic identities:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

Solution:

Given,

a² + b² = 970

ab = 483

Using the above given identities, we find

a² + b² = (a - b)² + 2ab

or, (a - b)² = (a² + b²) - 2ab

or, (a - b)² = 970 - 2 (483)

or, (a - b)² = 970 - 966

or, (a - b)² = 4

or, a - b = ± 2

∴ a - b = ± 2