Evaluate : $4 (2 x - 3)^{2} - 9 (y + 1)^{2}$

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Solution

$4 (2 x - 3)^{2} - 9 (y + 1)^{2}$

$4 (4 x^{2} + 9 - 12 x) - 9 (y^{2} + 1 + 2 y)$

$16 x^{2} + 36 - 48 x - 9 y^{2} - 9 - 18 y$

$16 x^{2} - 48 x - 9 y^{2} - 18 y + 27$

$16 x (x - 3) - 9 y (y - 2) + 27$

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lim n \to \infty \frac{1}{n^{4}} [1^{2} + (1^{2} + 2^{2}) + (1^{2} + 2^{2} + 3^{2}) + . . . . . . (1^{2} + 2^{2} + 3^{2} + . . . . n^{2})]

\frac{\sqrt{32} + \sqrt{48}}{\sqrt{8} + \sqrt{12}}

x

4^{2 x} = \frac{1}{32}

x,

4^{2 x} = \frac{1}{32}

Find $x$ , if $4^{2 x} = \frac{1}{32}$ .

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