Find the value of each of the following expressions :
$36 x^{2} + 49 y^{2} + 84 x y$ , when $x = \frac{1}{4}, y = \frac{2}{7}$

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Solution

A] $36 x^{2} + 49 y^{2} + 84 x y$
where $x = \frac{1}{4} y = \frac{2}{7}$
$\Rightarrow 36 (\frac{1}{4})^{2} + 49 (\frac{2}{7})^{2} + 84 \times \frac{1}{4} \times \frac{2}{7}$
= $36 \times \frac{1}{4} \times \frac{1}{4} + \frac{48 \times 2 \times 2}{7 \times 7} + 84 \times \frac{1}{4} \times \frac{2}{7}$
= $\frac{9}{4} + 4 + \frac{42}{7}$
= $\frac{9 + 16}{4} + \frac{42}{7} = \frac{25}{4} + \frac{42}{7}$
= $\frac{175 + 168}{28} = \frac{34}{28} = \frac{49}{4}$

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