Question

if x= 2-√3 then find the value of ( x+1/x)^3​

Answer 1

Answer:

64

Step-by-step explanation:

x= 2-√3

=> 1/x = $\frac{1}{2-\sqrt{3} }$

          = $\frac{1}{2-\sqrt{3} }$ * $\frac{2+\sqrt{3}}{2+\sqrt{3} }$

          = $\frac{2+\sqrt{3}}{2^2-\sqrt{3}^2 }$

          = $\frac{2+\sqrt{3}}{4-3 }$

          = 2+√3

so, (x + $\frac{1} {x}$ )³ = (2-√3 + 2+√3)³

                  = 4³

                  = 64