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Cube Numbers

If a + 2 b ...

Question

If $a + 2 b = 9 and a b = 7$ . Find the value of $a^{2} + 4 b^{2}$

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Solution

$a + 2 b = 9$ and $a b = 7$

Find value of $a^{2} + 4 b^{2}$

$(a + 2 b)^{2} = a^{2} + 4 b^{2} + 4 a b$

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

$= (9)^{2} - 4 (7)$

$= 81 - 28 = 53$ .

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