Question

What is the solution of √2x+4 - √x = 2
please show with work done!​

Answer 1

To solve the equation √2x+4 - √x = 2, we can first square both sides of the equation to eliminate the square roots.

Squaring both sides gives: (√2x+4)^2 - (√x)^2 = 2^2

Simplifying the left side gives: 2x+4 - x = 4

Next, we can add x to both sides of the equation to get:

2x+4 = 4 + x

then we can subtract 4 from both sides of the equation to get:

2x = x

then we can divide both sides by x

2 = 1

However, it is not possible to divide by zero, so x = 0 is not a valid solution.

This equation is an extraneous solution because the assumption that x is not equal to 0 led to a valid solution, but when x = 0, the equation is not defined.

Therefore, the solution of √2x+4 - √x = 2 is x = any value except 0.

Answer 2

x=1

Explanation:

To solve the equation, we'll need to get the square roots on one side and the non-square root terms on the other side.

First, we'll add √x to both sides to get:

√2x+4 - √x + √x = 2 + √x

√2x+4 = 2 + √x

Next, we'll square both sides to get rid of the square roots:

(√2x+4)^2 = (2 + √x)^2

2x+4 = 4 + 2√x + x

Then, we'll simplify the right side of the equation:

2x+4 = 4 + 2√x + x

2x+4 = 4 + x + 2√x

Now we'll subtract 4 from both sides

2x = x + 2√x

x = 2√x

Finally, we'll divide by x on both sides

1 = 2√x/x

x = √x

x = 1

Therefore, the solution of the equation is x=1