Question

The area of a circle is given by the expression $\pi x^2+6\pi x+9\pi$. Find the radius of the circle.

Answer 1

Area of the circle$=\pi r^2=\pi x^2+6\pi x+9\pi$

$\Rightarrow r^2=x^2+6x+9$

$\Rightarrow r^2=x^2+2\times 3x+3^2={(x+3)}^2$

$\Rightarrow r=x+3$

Hence radius of the circle is $x+3$ for $x\in R$