# Expansions-3

### From Homeworkwiki

**If a + b = 9 and a b = - 22, find : (i) a - b (ii) a ^{ 2 } - b ^{ 2 }**

**Solution:**

(i) (a + b) ^{ 2 } - (a - b) ^{ 2 } = 4 a b

=> (a - b) ^{ 2 } = (a + b) ^{ 2 } - 4 a b

= (9) ^{ 2 } - 4 X (-22) = 81 + 88 = 169

Therefore, **a - b** = ± √169 = **± 13**

(ii) a ^{ 2 } - b ^{ 2 } = (a + b) (a - b) = 9 X (± 13) = ** ±117**