Respuesta :
The simplified radical for the given equation is 2√3.
The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].
What are radicals?
Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.
To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:
[tex]\frac{3}{x} =\frac{x}{4}[/tex]
⇒x×x=3×4
⇒x²=12
⇒x=±√12
From this, we can see that the solutions for the equation are the positive and negative roots of 12.
By simplifying the radical, we get √12 = √(2² x 3) = 2√3
Therefore, the simplified radical for the given equation is 2√3.
To learn more about radicals visit:
https://brainly.com/question/1369233.
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