If a + b = 4 and ab = -12, find
(i) a – b
(ii) a2 – b2.
Answer :
(i) We know that
(a – b)2 = a2 + b2 – 2ab
It can be written as
(a – b)2 = a2 + b2 + 2ab – 4ab
(a – b)2 = (a + b)2 – 4ab
It is given that
a + b = 4 and ab = – 12
Substituting the values
(a – b)2 = 42 – 4 (-12)
By further calculation
(a – b)2 = 16 + 48 = 64
So we get
(a – b) = ± √64 = ± 8
(ii) We know that
a2 – b2 = (a + b) (a – b)
Substituting the values
a2 – b2 = 4 × ±8
a2 – b2 = ± 32
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