Question

Solve: √x+1=√x+6=1

Squaring both sides of the equation results in
which of the following?
x+1=x+6-1
x+1=x+6+1
O x+1=x+7+2√x+6
Ox+1=x+7-2√x+6

Answer 1

To correctly square the equation √x + 1 = 1, the square root is removed, resulting in the equation x + 1 = 1 which further simplifies to x = 0 after subtracting 1 from both sides.

Step-by-step explanation:

The student's equation seems to be misstated, and its structure is unclear from the question. However, addressing the original intent of squaring both sides of a square root equation, let's consider an equation structured as √x + 1 = 1. When you square both sides of this equation, you remove the square root, thus the equation becomes x + 1 = 1. To further solve it, you would subtract 1 from both sides resulting in x = 0. It's important to note that we ignored the supposed second equation √x + 6 = 1 as it does not properly fit into the first equation and seems to be a typo or error in the question.

If you have an equation like √x + a = √(x + b) and you square both sides, you would end up with x + a2 = x + b + 2√x(a), where a and b are constants.