Question

If x= 3+2√3 find the value of x²+1/x² and x⁴+1/x⁴​

Answer 1

Step-by-step explanation:

x-1/x = 3

(x-1/x )^2 = x^2+ 1/x^2- 2

(x - 1/x )^2 = (3)^2

so x^2+ 1/x^2 -2 = 9

so x^2 + 1^2 will be 9+2 = 11

x^4 + 1/ x ^4 will be x^2+ 1/ x^2 whole square

so by squaring on both sides we get (x)^2 + (1/ x)^2 =(11)^2

so x^4 + 1/ x^4 +2 = 121

x ^4 + 1/ x ^4 will be 121-2=119