Is x=18 in the solution set of the radical equation 4 root of x minus 2 end root plus 4 equals 2 ? Tell why or why not.
To determine if x=18 is in the solution set of the radical equation, we can substitute the value of x=18 into the equation and check if the equation holds true or not.
Given equation: 4√x - 2√x + 4 = 2
Let's substitute x=18 into the equation:
4√(18) - 2√(18) + 4 = 2
Now, let's simplify the equation:
4√(18) = 2√(18) - 2
Simplifying further:
2√(18) = 2
Next, divide both sides of the equation by 2:
√(18) = 1
Now, square both sides of the equation to eliminate the square root:
18 = 1^2
Simplifying:
18 = 1
However, this statement is not true. Therefore, x=18 is not a solution of the equation.
Therefore, x=18 is not in the solution set of the radical equation 4√x - 2√x + 4 = 2.
To determine if x=18 is in the solution set of the radical equation, we need to solve the equation and substitute x=18 into it.
The given radical equation is:
4√x - 2√x + 4 = 2
To solve this equation, we'll start by isolating the radicals on one side of the equation and moving the other terms to the opposite side:
4√x - 2√x = 2 - 4
Simplifying:
2√x = -2
Now, let's square both sides of the equation to eliminate the square root:
(2√x)^2 = (-2)^2
4x = 4
Next, divide both sides of the equation by 4:
x = 1
So, the solution to the radical equation is x = 1, not x = 18.
Therefore, x=18 is NOT in the solution set of the given equation.
all those words! How about
4√(x-2)+4=2
18 is not in the domain, nor is any other real number, because √ is positive. There's no way to add a positive value to 4 and end up with 2.