Question

The solution of the equation $(1+x+x^2+...+x^{11})=(x+3)+\frac{x^{12}}{x-1}$ is

• A. $\sqrt{3}-1$
• B. $1-\sqrt{3}$
• C. $\sqrt{3}+1$
• D. $-1\pm \sqrt{3}$

Answer 1

Answer: (D)

$-1\pm \sqrt{3}$

Given,

$(1+x+x^2+...+x^{11})=\frac{x+3}{1}+\frac{x^{12}}{x-1}$

$\frac{x^{12}-1}{x-1}=\frac{x+3}{1}+\frac{x^{12}}{x-1}$

$\Rightarrow \frac{-1}{x-1}=\frac{x+3}{1}$

$\Rightarrow x^2+2x-2=0$

$\Rightarrow x=\frac{-2\pm \sqrt{12}}{2}=-1\pm \sqrt{3}$