Question

What is the solution to the equation below?

square root 2x/ square root x - 2 = 2

Answer 1

x=4

Explanation:

`(√(2x) )/(√(x-2))=2`

Multiply both sides by
`√(x-2)` :

`\implies √(2x)=2√(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`

Answer 2

`x= 4`

Explanation:

`(√(2x))/(√(x-2)\:)=2` [ bring √(x - 2) to the opposite side ]

`√(2x) = 2√(x-2)`

`(√(2x) )^(2) = (2√(x-2))^2` [ square both sides ]

`2x = 4(x-2)`

`2x=4x-8`

`2x - 4x = -8`

`-2x = -8`

`x= 4`