Solve: 4 sqrt (x) = 8 + 2 sqrt (x)
a) (-4)
b) (16)
c) none
d) (4)
c
It is c none for sure I have tried it two different ways
4√x = 8 + 2√x
Subtract 2√x from both sides.
2√x = 8
Divide both sides by 2
√x = 4
x = 16
To solve the equation 4√(x) = 8 + 2√(x), we need to gather the terms involving the square root on one side of the equation and the constants on the other side. Here's how you can do it step by step:
1. Start by subtracting 2√(x) from both sides of the equation to isolate the terms involving the square root:
4√(x) - 2√(x) = 8 + 2√(x) - 2√(x)
This simplifies to:
2√(x) = 8
2. Next, subtract 8 from both sides to isolate the term involving the square root:
2√(x) - 8 = 0
3. Now, we have a linear equation in terms of √(x). To solve for √(x), add 8 to both sides of the equation:
2√(x) = 8
This simplifies to:
2√(x) + 8 = 8 + 8
2√(x) + 8 = 16
4. Then, divide both sides of the equation by 2 to solve for √(x):
(2√(x) + 8) / 2 = 16 / 2
This simplifies to:
√(x) + 4 = 8
5. Lastly, subtract 4 from both sides of the equation to find the value of √(x):
√(x) + 4 - 4 = 8 - 4
This simplifies to:
√(x) = 4
To find the value of x, we need to square both sides of the equation to eliminate the square root:
(√(x))^2 = 4^2
This simplifies to:
x = 16
Therefore, the solution to the equation 4√(x) = 8 + 2√(x) is x = 16. Thus, the answer is (b) 16.