Expansions-3

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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

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