Find the values of x for which the expression equals zero.
-$$\sqrt { 4 - x ^ { 2 } } - x \left( \frac { 1 } { 2 } \right) \frac { 1 } { \sqrt { 4 - x ^ { 2 } } } ( 2 x )$$
A) $\{ \pm \sqrt { 2 } \}$
B) $\{ \sqrt { 2 } , 2 \}$
C) $\{ \pm 2 \}$
D) $\{ \pm \sqrt { 2 } , \pm 2 \}$

Question

Quizplus · Accepted Answer

The expression simplifies to $\sqrt{4-x^2} - x^2/\sqrt{4-x^2}$. Factoring out $\sqrt{4-x^2}$, we get $\sqrt{4-x^2}(1 - x^2/(4-x^2))$. Simplifying inside the parenthesis gives $1 - x^2/(4-x^2) = (4-x^2-x^2)/(4-x^2) = (4-2x^2)/(4-x^2)$. Setting the numerator equal to zero gives $4-2x^2 = 0$, solving for $x$ yields $x^2 = 2$, so $x = \pm \sqrt{2}$.

Find the Values of X for Which the Expression Equals 4−x2−x(12)14−x2(2x)\sqrt { 4 - x ^ { 2 } } - x \left( \frac { 1 } { 2 } \right) \frac { 1 } { \sqrt { 4 - x ^ { 2 } } } ( 2 x )4−x2​−x(21​)4−x2​1​(2x)

Find the Values of X for Which the Expression Equals $\sqrt { 4 - x ^ { 2 } } - x \left( \frac { 1 } { 2 } \right) \frac { 1 } { \sqrt { 4 - x ^ { 2 } } } ( 2 x )$