**If a + b = 4 and ab = -12, find**

(i) a – b

(ii) a^{2} – b^{2}.

**Answer :**

##### (i) We know that

**(a – b) ^{2} = a^{2} + b^{2} – 2ab**

It can be written as

(a – b)^{2} = a^{2} + b^{2} + 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} = 4^{2} – 4 (-12)

By further calculation

(a – b)^{2} = 16 + 48 = 64

So we get

(a – b) = ± √64 = ± 8

##### (ii) We know that

**a ^{2} – b^{2} = (a + b) (a – b)**

Substituting the values

a^{2} – b^{2} = 4 × ±8

a^{2} – b^{2} = ± 32

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