Question

if
$a = \frac{2 - \sqrt{3} }{2}$
then find the value of
${a}^{2} + \frac{1}{ {a}^{2} }$
​

Answer 1

Step-by-step explanation:

a=(2-√3)/2

a^2=(2-√3)^2/4

=(4+3-4√3)/4

=(7-4√3)/4

1/a^2=4/(7-4√3)

=4(7+4√3)/(7-4√3)(7+4√3)

=4(7+4√3)/(7^2-4√3^2)

=4(7+4√3)/(49-48)

=4(7+4√3)

so,

a^2+1/a^2

=(7-4√3)/4+4(7+4√3)

={(7-4√3)+16(7+4√3)}/4

=(7-4√3+112+64√3)/4

=(119+60√3)/4

=119/4+15√3