If a - b = 6 and ab = 16; find $a^{2} + b^{2}$

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Solution

$(a - b)^{2} = a^{2} + b^{2} - 2 a b \Rightarrow (6)^{2} = a^{2} + b^{2} - 2 \times 16 \Rightarrow 36 = a^{2} + b^{2} - 32 \Rightarrow 36 + 32 = a^{2} + b^{2} \Rightarrow 68 = a^{2} + b^{2} ∴ a^{2} + b^{2} = 68$ .

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