Solve the radical equation, if possible. $$6 = \sqrt { x ^ { 2 } + 3 } - x$$
A) $\left\{ - \frac { 11 } { 4 } \right\}$
B) $\left\{ \frac { 13 } { 2 } \right\}$
C) $\left\{ \frac { 13 } { 4 } \right\}$
D) \{ \}

Question

Quizplus · Accepted Answer

To solve the equation $6 = \sqrt { x ^ { 2 } + 3 } - x$, we first isolate the square root term: $\sqrt { x ^ { 2 } + 3 } = x + 6$. Squaring both sides gives $x^2 + 3 = x^2 + 12x + 36$. Simplifying, we get $0 = 12x + 33$, leading to $x = -\frac{33}{12} = -\frac{11}{4}$.

Solve the Radical Equation, If Possible 6=x2+3−x6 = \sqrt { x ^ { 2 } + 3 } - x6=x2+3​−x

Solve the Radical Equation, If Possible $6 = \sqrt { x ^ { 2 } + 3 } - x$