Question

Find the value of a-b when a+b=9and ab=7

Answer 1

Given:

(a + b)= 9

ab = 7

To Find

The value of a - b

Solution:

⇒ (a + b)² = (9)²                [squaring both sides]

⇒ a² + b² + 2ab = 81

⇒ a² + b² = 81 - 2(7)           [ it is given that 'ab' is 7]

⇒ a² + b² = 81 - 14

⇒ a² + b² = 67 ..(i)

Now,

(a - b)² = a² + b² - 2ab

           = 67 - 2(7)          [ from (i)]

           = 67 - 14

           = 53

So, a - b = √9

              = ± 3

Therefore, the value of a - b is √9 or ± 3.