Question

What is the solution to the equation below?

Answer 1

Answer:

$x= 4$

Step-by-step explanation:

$\frac{\sqrt{2x}}{\sqrt{x-2}\:}=2$                       [ bring √(x - 2) to the opposite side ]

$\sqrt{2x} = 2\sqrt{x-2}$          

$(\sqrt{2x} )^{2} = (2\sqrt{x-2})^2$      [ square both sides ]

$2x = 4(x-2)$  

$2x=4x-8$

$2x - 4x = -8$

$-2x = -8$

$x= 4$

Answer 2

Answer:

x=4

Step-by-step explanation:

$\dfrac{\sqrt{2x} }{\sqrt{x-2}}=2$

Multiply both sides by $\sqrt{x-2}$ :

$\implies \sqrt{2x}=2\sqrt{x-2}$

Square both sides:

$\implies 2x=4(x-2)\\\\\implies 2x=4x-8$

Add 8 to both sides:

$\implies 2x+8=4x$

Subtract $2x$ from both sides:

$\implies 8=2x$

Divide both sides by 4:

$\implies x=4$