The equation is [tex]\sqrt{x-2 \\ \\[/tex] -[tex]\sqrt{2x}[/tex] = [tex]\sqrt{x +2}[/tex]
Solution
Step 1:
Take square on both sides, we get
3x - 2[tex]\sqrt{x-2}[/tex][tex]\sqrt2{x}[/tex] -2 = x +2
Step 2:
Subtract 3x - 2 from both sides, we get
-2[tex]\sqrt{x-2} \sqrt{2x} = -2x + 4[/tex]
Step 3:
Again, square on both sides in order to get rid of the square root from the above equation, we get
[tex]8x^{2}-16x = 4x^{2} -16x +16[/tex]
Now we have to simplify it,
[tex]4x^{2} -16 = 0[/tex]
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
