Question

If x= (2 + √3) find the value of (x2+1/x2) explain A) 14 B) 13 C)-14 D)12​

Answer 1

Answer:

The correct answer is option (A) .

Step-by-step explanation:

Given $x=2+\sqrt 3$

         $\Rightarrow x-2=\sqrt 3$

square both sides

         $\Rightarrow (x-2)^2=(\sqrt3)^2\\\Rightarrow x^2-4x+4=3\\\Rightarrow x^2-4x+1=0\\\Rightarrow x^2+1=4x\\\Rightarrow \frac{x^2+1}{x}=\frac{4x}{x}\\\Rightarrow x+\frac{1}{x}=4$

Again square both sides

         $\Rightarrow (x+\frac{1}{x})^2=4^2\\\Rightarrow x^2+\frac{1}{x^2}+2(x)(\frac{1}{x})=16\\\Rightarrow x^2+\frac{1}{x^2}+2=16\\\therefore x^2+\frac{1}{x^2}=16-2=14$