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Expansion of (x+y)^2

If a2 + b2 = ...

Question

If $a^{2} + b^{2} = 41 a n d a b = 4,$ find :

(i) (a - b)

(ii) (a + b)

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Solution

(i) $(a - b)^{2} = a^{2} + b^{2} - 2 a b = 41 - 2 (4) = 41 - 8 = 33 ∴ a - b = \sqrt{33}$

(ii) $(a + b)^{2} = a^{2} + b^{2} + 2 a b = 41 + 2 (4) = 41 + 8 = 49 \Rightarrow (a + b)^{2} = 49 ∴ a + b = 7$

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