Solve the equation.
-$\sqrt{\mathrm{x}+3}=\mathrm{x}-3$
A) $\{6\}$
B) $\{1,6\}$
C) $\{1,13\}$
D) $\{6,13\}$

Question

Quizplus · Accepted Answer

Squaring both sides of the equation $\sqrt{x+3}=x-3$ gives $x+3=(x-3)^2$. Simplifying, we get $x+3=x^2-6x+9$, leading to $x^2-7x+6=0$. Factoring, we find $(x-1)(x-6)=0$, so $x=1$ or $x=6$. However, substituting $x=1$ back into the original equation gives a contradiction ($\sqrt{4} \neq -2$), so the only solution that works in the original equation is $x=6$.

Solve the Equation x+3=x−3\sqrt{\mathrm{x}+3}=\mathrm{x}-3x+3​=x−3 A) {6}\{6\}{6} B) {1,6}\{1,6\}{1,6} C) {1,13}\{1,13\}{1,13} D) {6,13}\{6,13\}{6,13}

Solve the Equation $\sqrt{\mathrm{x}+3}=\mathrm{x}-3$ A) $\{6\}$ B) $\{1,6\}$ C) $\{1,13\}$ D) $\{6,13\}$