Question

If x = 0.50, then the value of the expression $\left\{\right(1+x+x^2)+\frac{x^3}{1-x}\}$ is

• A. 4
• B. 2
• C. 1.5
• D. 1

Answer 1

The correct option is B 2

Given, $\left\{\right(1+x+x^2)+\frac{x^3}{1-x}\}$
$=\frac{(1-x)(1+x+x^2)+x^3}{1-x}$
$=\frac{(1-x^3)+x^3}{1-x}$ [$\because a^3-b^3=(a-b)(a^2+b^2+ab)$]
$=\frac{1}{1-x}$
$=\frac{1}{1-0.50}$ Given x=0.50
$=\frac{1}{0.50}$
$=2$
Option B is correct.