If $a + 2 b = 5$ , and $a b = 2$ find $a^{2} + 4 b^{2}$

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Solution

Given, $a + 2 b = 5$ , and $a b = 2$ .
Now,
$a^{2} + 4 b^{2}$
$= (a + 2 b)^{2} - 2. a .2 b$
$= 5^{2} - 4 a b$
$= 25 - 4 \times 2$ [ Using the given values]
$= 17$ .

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