If x=5+2 root 6 then find the value of x^2+1/x^2
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x=5+2√6
1/x=1/5+2√6×5-2√6/5-2√6
=5-2√6/5^2-2√6^2
=5-2√6/25-24
=5-2√6
now, x^2+(1/x)^2
=(5+2√6)^2+ (5-2√6)^2
=(25+24+2×5×2√6)+(25+24-2×5×2√6)
=25+24+20√6+25+24-20√6
=25+24+25+24. (cancle20√6-20√6)
=50+48
=98
1/x=1/5+2√6×5-2√6/5-2√6
=5-2√6/5^2-2√6^2
=5-2√6/25-24
=5-2√6
now, x^2+(1/x)^2
=(5+2√6)^2+ (5-2√6)^2
=(25+24+2×5×2√6)+(25+24-2×5×2√6)
=25+24+20√6+25+24-20√6
=25+24+25+24. (cancle20√6-20√6)
=50+48
=98
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