If x=5-2root6,find x^2+1/x^2

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Solution

X=5-2√6
∴, x²=(5-2√6)²
=25-2.5.2√6+24=49-20√6
1/x²=1/(5-2√6)²
=1/(49-20√6)
=(49+20√6)/(49-20√6)(49+20√6)
=(49+20√6)/(2401-2400)
=49+20√6
∴, x²+1/x²
=49-20√6+49+20√6=98

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