Question

If=2+√3,then find the value of x^4+1/x^4

Answer 1

Step-by-step explanation:

x=2+√3

x^2=(2+√3)^2

= 4+2√3+3

x^2 =7+2√3

(x^2)^2=(7+2√3)^2

x^4=49+2*7*(2√3)+(2√3)^2

=49+28√3+12

=61+28√3

1/x=1/(2+√3)

1/x=1/2+√3 *(2-√3 / 2-√3)

=(2-√3) / (4-3)

=2-√3

1/x^2=(2-√3)^2

= 4-2√3+3

x^2 =7-2√3

(x^2)^2=(7-2√3)^2

x^4=49-2*7*(2√3)+(2√3)^2

=49-28√3+12

=61-28√3

x^4+1/x^4 =61+28√3 + 61-28√3=61+61=122