Question

select whether the equation has a solution or not, square root x-2- square root 2x= square root x+2 (a. roots b. no roots)

Answer 1

The equation is $\sqrt{x-2$ -$\sqrt{2x}$ = $\sqrt{x +2}$

Solution

Step 1:

Take square on both sides, we get

3x - 2$\sqrt{x-2}$$\sqrt2{x}$ -2 = x +2

Step 2:

Subtract 3x - 2 from both sides, we get

-2$\sqrt{x-2} \sqrt{2x} = -2x + 4$

Step 3:

Again, square on both sides in order to get rid of the square root from the above equation, we get

$8x^{2}-16x = 4x^{2} -16x +16$

Now we have to simplify it,

$4x^{2} -16 = 0$

Step 4:

Now we have to solve this quadratic equation, in order to get the solution.

We get x = 2 and x = -2, When we verifying solution in the original given equation, the solution does not satisfy the equation.

Reason: We get negative number in the square root.

Therefore, it has no Roots.

Answer: b) No roots