If x=5+2√6 then show that x2+1/x2=98?
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x = 5 + 2√6
1/x =1/[5 + 2√6] =5 -2√6
x2 +1/x2 =(5+2√6)^2 +(5-2√6)^2
= 5^2 +[2√6]^2 +2(5)(2√6] +5^3 +(2√6)^2 -2(5)[2√6]
=25 +24 +20√6 +25+24-20√6
=98
1/x =1/[5 + 2√6] =5 -2√6
x2 +1/x2 =(5+2√6)^2 +(5-2√6)^2
= 5^2 +[2√6]^2 +2(5)(2√6] +5^3 +(2√6)^2 -2(5)[2√6]
=25 +24 +20√6 +25+24-20√6
=98
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