frac{12}{3 + sqrt{5} - 2sqrt{2}} = | vedclass

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Question

(C) Let $x = \frac{12}{3 + \sqrt{5} - 2\sqrt{2}}$.To rationalize the denominator,we group the terms as $(3 + \sqrt{5}) - 2\sqrt{2}$.Multiply the numer

Vedclass · Accepted Answer

$1 + \sqrt{5} + \sqrt{10} - \sqrt{2}$

Vedclass · Answer

(C) Let $x = \frac{12}{3 + \sqrt{5} - 2\sqrt{2}}$.To rationalize the denominator,we group the terms as $(3 + \sqrt{5}) - 2\sqrt{2}$.Multiply the numerator and denominator by $(3 + \sqrt{5}) + 2\sqrt{2}$:$x = \frac{12(3 + \sqrt{5} + 2\sqrt{2})}{(3 + \sqrt{5})^2 - (2\sqrt{2})^2}$$x = \frac{12(3 + \sqrt{5} + 2\sqrt{2})}{(9 + 5 + 6\sqrt{5}) - 8}$$x = \frac{12(3 + \sqrt{5} + 2\sqrt{2})}{6 + 6\sqrt{5}}$$x = \frac{12(3 + \sqrt{5} + 2\sqrt{2})}{6(1 + \sqrt{5})} = \frac{2(3 + \sqrt{5} + 2\sqrt{2})}{1 + \sqrt{5}}$Rationalize again by multiplying by $(\sqrt{5} - 1)$:$x = \frac{2(3 + \sqrt{5} + 2\sqrt{2})(\sqrt{5} - 1)}{5 - 1} = \frac{2(3\sqrt{5} - 3 + 5 - \sqrt{5} + 2\sqrt{10} - 2\sqrt{2})}{4}$$x = \frac{2(2 + 2\sqrt{5} + 2\sqrt{10} - 2\sqrt{2})}{4} = \frac{4(1 + \sqrt{5} + \sqrt{10} - \sqrt{2})}{4}$$x = 1 + \sqrt{5} + \sqrt{10} - \sqrt{2}$.

$\frac{12}{3 + \sqrt{5} - 2\sqrt{2}} = $

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