which equation results from isolating a radical term and squaring both sides of the equation for the…

which equation results from isolating a radical term and squaring both sides of the equation for the equation $sqrt{c - 2}-sqrt{c}=5$?\n$c - 2=25 + c$\n$c - 2=25 - c$\n$c - 2=25 + c-10sqrt{c}$\n$c - 2=25 + c + 10sqrt{c}$

which equation results from isolating a radical term and squaring both sides of the equation for the equation $sqrt{c - 2}-sqrt{c}=5$?\n$c - 2=25 + c$\n$c - 2=25 - c$\n$c - 2=25 + c-10sqrt{c}$\n$c - 2=25 + c + 10sqrt{c}$

Answer

Explanation:

Step1: Isolate a radical term

Isolate $\sqrt{c - 2}$ in the equation $\sqrt{c - 2}-\sqrt{c}=5$. We get $\sqrt{c - 2}=5+\sqrt{c}$.

Step2: Square both sides

Square both sides of the equation $\sqrt{c - 2}=5+\sqrt{c}$. According to the formula $(a + b)^2=a^{2}+2ab + b^{2}$, where $a = 5$ and $b=\sqrt{c}$, we have $(\sqrt{c - 2})^2=(5+\sqrt{c})^2$. So $c - 2=25 + 10\sqrt{c}+c$.

Answer:

$c - 2=25 + c+10\sqrt{c}$ (the fourth option)