Solve x^-1*sqrt{3x}=4

$$x ^ { - 1 } \times \sqrt { 3 x } = 4$$

Solve for x

$$x=\frac{3}{16}=0.1875$$

Solution Steps

Reorder the terms.

$$\frac{1}{x}\sqrt{3x}=4$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$1\sqrt{3x}=4x$$

Subtract 4x from both sides.

$$1\sqrt{3x}-4x=0$$

Reorder the terms.

$$-4x+\sqrt{3x}=0$$

Subtract -4x from both sides of the equation.

$$\sqrt{3x}=4x$$

Square both sides of the equation.

$$\left(\sqrt{3x}\right)^{2}=\left(4x\right)^{2}$$

Calculate \sqrt{3x} to the power of 2 and get 3x.

$$3x=\left(4x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$3x=4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$3x=16x^{2}$$

Subtract 16x^{2} from both sides.

$$3x-16x^{2}=0$$

Factor out x.

$$x\left(3-16x\right)=0$$

To find equation solutions, solve x=0 and 3-16x=0.

$$x=0 x=\frac{3}{16}$$

Substitute 0 for x in the equation x^{-1}\sqrt{3x}=4. The expression is undefined.

$$0^{-1}\sqrt{3\times 0}=4$$

Substitute \frac{3}{16} for x in the equation x^{-1}\sqrt{3x}=4.

$$\left(\frac{3}{16}\right)^{-1}\sqrt{3\times \frac{3}{16}}=4$$

Simplify. The value x=\frac{3}{16} satisfies the equation.

$$4=4$$

Equation \sqrt{3x}=4x has a unique solution.

$$x=\frac{3}{16}$$