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Polynomial and Its General Form

If a+b =5 and...

Question

If a+b =5 and $a^{2} + b^{2} = 13$ , find ab.

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Solution

$\begin{matrix} W e h a v e a + b = 5 b y s q u a r i n g b o t h s i d e s {(a + b)}^{2} = 5^{2} a^{2} + b^{2} + 2 a b = 25 13 + 2 a b = 25 2 a b = 25 - 13 2 a b = 12 ∴ a b = 6 H e n c e, t h e v a l u e o f a b i s 6. \end{matrix}$

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a^{2} + b^{2} = 13

a b = 6

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a = \frac{\sqrt{5} + 1}{\sqrt{5} - 1}

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Q. If a + b = 5 and ab = 6, find

a^{2} + b^{2}

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