Question

x=4+√5 then find out the value of (x^2+(1/x^2))

Answer 1

1/x=1/4+_/5

=1/4+_/5×4-_/5/4-_/5

=4-_/5/11

x+1/x=4+_/5+4-_/5/11

=48-10_/5/11

x^2+1/x^2=(48-10_/5/11)^2

=x^2+2+1/x^2=2304-500/121

=x^2+1/x^2=1804/121-2

=x^2+1/x^2=1562/121

Answer 2

$x {}^{2} + 1 \div x {}^{2} =( x + y) {}^{2} - 2 \times xy$

$(4 + \sqrt{5} + 4 - \sqrt{5}) {}^{2} - 2 \times 4 + \sqrt{5} \times 4 - \sqrt{5}$

$(8) {}^{2} - 2(4 {}^{2} - \sqrt{5 {)}^{2} }$

64-2(16-5)

62(11)

682ans.

pls see whether ans is right but process is correct ...

and sorry if ans. gets wrong...