If x=√5+2,then find the value of x^2+1/x^2
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Step-by-step explanation:
- x^2=(√5+2)^2
=5+4+2√5
=9+2√5 ..... i
- 1/x^2=1/(9+2√5)
=(9-2√5)/(9)^2-(2√5)^2
=(9-2√5)/(81-20)
=(9-2√5)/61 ....... ii
- adding i and ii
(9+2√5) +(9-2√5) /61
=9+2√5+9/61-2√5/61
=9+9/61+2√5+2√5/61
=(549+9)/61+(122√5+2√5)/61
=558/61+124√5/61 Or (558+124√5)/61
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