Question

If x=√5+2,then find the value of x^2+1/x^2​

Answer 1

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