Simplify :
26−2−36+2\dfrac{\sqrt{2}}{\sqrt{6} - \sqrt{2}} - \dfrac{\sqrt{3}}{\sqrt{6} + \sqrt{2}}6−22−6+23
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Solving,
⇒26−2−36+2⇒2(6+2)−3(6−2)(6−2)(6+2)⇒12+2−18+6(6)2−(2)2⇒23+2−32+66−2⇒23+2−32+64.\Rightarrow \dfrac{\sqrt{2}}{\sqrt{6} - \sqrt{2}} - \dfrac{\sqrt{3}}{\sqrt{6} + \sqrt{2}} \\[1em] \Rightarrow \dfrac{\sqrt{2}(\sqrt{6} + \sqrt{2}) - \sqrt{3}(\sqrt{6} - \sqrt{2})}{(\sqrt{6} - \sqrt{2})(\sqrt{6} + \sqrt{2})} \\[1em] \Rightarrow \dfrac{\sqrt{12} + 2 - \sqrt{18} + \sqrt{6}}{(\sqrt{6})^2 - (\sqrt{2})^2} \\[1em] \Rightarrow \dfrac{2\sqrt{3} + 2 - 3\sqrt{2} + \sqrt{6}}{6 - 2} \\[1em] \Rightarrow \dfrac{2\sqrt{3} + 2 - 3\sqrt{2} + \sqrt{6}}{4}.⇒6−22−6+23⇒(6−2)(6+2)2(6+2)−3(6−2)⇒(6)2−(2)212+2−18+6⇒6−223+2−32+6⇒423+2−32+6.
Hence, solution = 23+2−32+64\dfrac{2\sqrt{3} + 2 - 3\sqrt{2} + \sqrt{6}}{4}423+2−32+6.
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Find the values of 'a' and 'b':
33−2=a3−b2\dfrac{3}{\sqrt{3} - \sqrt{2}} = a\sqrt{3} - b\sqrt{2}3−23=a3−b2
2223+1+1723−1\dfrac{22}{2\sqrt{3} + 1} + \dfrac{17}{2\sqrt{3} - 1}23+122+23−117
If x = 5−25+2 and y=5+25−2\dfrac{\sqrt{5} - 2}{\sqrt{5} + 2} \text{ and } y = \dfrac{\sqrt{5} + 2}{\sqrt{5} - 2}5+25−2 and y=5−25+2; find :
(i) x2
(ii) y2
(iii) xy
(iv) x2 + y2 + xy
If m = 13−22 and n=13+22\dfrac{1}{3 - 2\sqrt{2}} \text{ and } n = \dfrac{1}{3 + 2\sqrt{2}}3−221 and n=3+221, find :
(i) m2
(ii) n2
(iii) mn
