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What is the solution to the equation below? square root 2x/ square root x - 2 = 2


What is the solution to the equation below? square root 2x/ square root x - 2 = 2

kaitlynbrace4214 kaitlynbrace4214    2   14.02.2022 06:30    5

Answers
joeykyle05 joeykyle05  14.02.2022 06:30

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

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innocentman69 innocentman69  14.02.2022 06:30

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

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