Solve \sqrt{1 x^{3}} \sqrt{x}-2x^{\frac{1}{4}}\left(1 x^{3}\right)^{\frac{1}{4}}

Question

Simplify the expression

Solution

x^{2} - 2 x

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Factor

x (x - 2)

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Find the roots of the algebra expression

x_{1} = 0, x_{2} = 2

Evaluate

1 \times x^{3} \times x - 2 x^{\frac{1}{4}} (1 \times x^{3})^{\frac{1}{4}}

To find the roots of the expression,set the expression equal to 0

1 \times x^{3} \times x - 2 x^{\frac{1}{4}} (1 \times x^{3})^{\frac{1}{4}} = 0

Find the domain

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1 \times x^{3} \times x - 2 x^{\frac{1}{4}} (1 \times x^{3})^{\frac{1}{4}} = 0, x \geq 0

Calculate

1 \times x^{3} \times x - 2 x^{\frac{1}{4}} (1 \times x^{3})^{\frac{1}{4}} = 0

Any expression multiplied by 1 remains the same

1 \times x^{3} \times x - 2 x^{\frac{1}{4}} (x^{3})^{\frac{1}{4}} = 0

Any expression multiplied by 1 remains the same

x^{3} \times x - 2 x^{\frac{1}{4}} (x^{3})^{\frac{1}{4}} = 0

Simplify the root

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x x \times x - 2 x^{\frac{1}{4}} (x^{3})^{\frac{1}{4}} = 0

Evaluate the power

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x x \times x - 2 x^{\frac{1}{4}} \times x^{\frac{3}{4}} = 0

Multiply the terms

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x^{2} - 2 x^{\frac{1}{4}} \times x^{\frac{3}{4}} = 0

Multiply

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x^{2} - 2 x = 0

Factor the expression

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x (x - 2) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 x - 2 = 0

Solve the equation for x

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x = 0 x = 2

Check if the solution is in the defined range

x = 0 x = 2, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = 2

Solution

x_{1} = 0, x_{2} = 2

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