Question

The sum of a number and its square is one half times their difference . Find the number

• A. $x=\sqrt{5}$
• B. $x=\sqrt{2}$
• C. $x=\sqrt{3}$
• D. $x=\sqrt{7}$

Answer 1

The correct option is

A

$x=5$

Let the number be $x$

then its square is $x^2$

Given that $x+x^2$ = 1$\frac{1}{2}(x^2-x)$

$x+x^2$ = $\frac{3}{2}(x^2-x)$

$2x+2x^2$ = $3(x^2-x)$

$-x^2=-5x$

$x^2-5x=0$

$x(x-5)=0$

$\therefore x=5\text{or}0$ is the required values.