Dear Student, a=5+26Squaring both sides, a2 = 5+262[Using (a+b)2 = a2+b2+2ab]a2 = 25+24+206a2 = 49+206Also, given b = 1aSquaring both sides, b2 = 1a2b2 = 149+206b2 = 149+206×49-20649-206[Using a2-b2 = (a-b)(a+b)]b2 = 49-206492-2062b2 = 49-2062401-2400b2 = 49-206Now, a2+b2 =49+206+ 49-206a2+b2 = 98 Regards

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Dear Student,

a = 5 + 2 \sqrt{6} Squaring both sides, a^{2} = {(5 + 2 \sqrt{6})}^{2} [Using {(a + b)}^{2} = a^{2} + b^{2} + 2 ab] a^{2} = 25 + 24 + 20 \sqrt{6} a^{2} = 49 + 20 \sqrt{6} Also, given b = \frac{1}{a} Squaring both sides, b^{2} = \frac{1}{a^{2}} b^{2} = \frac{1}{(49 + 20 \sqrt{6})} b^{2} = \frac{1}{(49 + 20 \sqrt{6})} \times \frac{49 - 20 \sqrt{6}}{49 - 20 \sqrt{6}} [Using a^{2} - b^{2} = (a - b) (a + b)] b^{2} = \frac{49 - 20 \sqrt{6}}{{(49)}^{2} - {(20 \sqrt{6})}^{2}} b^{2} = \frac{49 - 20 \sqrt{6}}{2401 - 2400} b^{2} = 49 - 20 \sqrt{6} Now, a^{2} + b^{2} = 49 + 20 \sqrt{6} + 49 - 20 \sqrt{6} a^{2} + b^{2} = 98

Regards

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