Answer :
To determine which equation results from isolating a radical term and squaring both sides for the equation \(\sqrt{c-2} - \sqrt{c} = 5\), follow these steps:
1. Start with the given equation:
[tex]\[ \sqrt{c-2} - \sqrt{c} = 5 \][/tex]
2. Isolate one of the radical terms:
[tex]\[ \sqrt{c-2} = 5 + \sqrt{c} \][/tex]
3. Square both sides of the equation to eliminate the square roots:
[tex]\[ (\sqrt{c-2})^2 = (5 + \sqrt{c})^2 \][/tex]
4. Rewrite the squared terms:
[tex]\[ c-2 = (5 + \sqrt{c})^2 \][/tex]
5. Expand the right side:
[tex]\[ c - 2 = 25 + 10 \sqrt{c} + c \][/tex]
With these steps, we obtain the resulting equation:
[tex]\[ c - 2 = 25 + 10 \sqrt{c} + c \][/tex]
The correct answer is:
[tex]\[ c - 2 = 25 + c + 10 \sqrt{c} \][/tex]
1. Start with the given equation:
[tex]\[ \sqrt{c-2} - \sqrt{c} = 5 \][/tex]
2. Isolate one of the radical terms:
[tex]\[ \sqrt{c-2} = 5 + \sqrt{c} \][/tex]
3. Square both sides of the equation to eliminate the square roots:
[tex]\[ (\sqrt{c-2})^2 = (5 + \sqrt{c})^2 \][/tex]
4. Rewrite the squared terms:
[tex]\[ c-2 = (5 + \sqrt{c})^2 \][/tex]
5. Expand the right side:
[tex]\[ c - 2 = 25 + 10 \sqrt{c} + c \][/tex]
With these steps, we obtain the resulting equation:
[tex]\[ c - 2 = 25 + 10 \sqrt{c} + c \][/tex]
The correct answer is:
[tex]\[ c - 2 = 25 + c + 10 \sqrt{c} \][/tex]
