Solve x^(5/3)-x^(2/3)-20x^(-1/3)

Question

Simplify the expression

\frac{x ^{2} 3 x ^{2} - 3 x ^{2} \times x - 20 3 x ^{2}}{x}

Show Solution

x_{1} = - 4, x_{2} = 5

Evaluate

x^{\frac{5}{3}} - x^{\frac{2}{3}} - 20 x^{- \frac{1}{3}}

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

x^{\frac{5}{3}} - x^{\frac{2}{3}} - 20 x^{- \frac{1}{3}} = 0

Find the domain

x^{\frac{5}{3}} - x^{\frac{2}{3}} - 20 x^{- \frac{1}{3}} = 0, x \neq = 0

Calculate

x^{\frac{5}{3}} - x^{\frac{2}{3}} - 20 x^{- \frac{1}{3}} = 0

Rewrite the expression

More Steps

x^{\frac{5}{3}} - x^{\frac{2}{3}} - \frac{20}{x ^{\frac{1}{3}}} = 0

Multiply both sides of the equation by LCD

(x^{\frac{5}{3}} - x^{\frac{2}{3}} - \frac{20}{x ^{\frac{1}{3}}}) x^{\frac{1}{3}} = 0 \times x^{\frac{1}{3}}

Simplify the equation

More Steps

x^{\frac{4}{3}} 3 x^{2} - x - 20 = 0 \times x^{\frac{1}{3}}

Any expression multiplied by 0 equals 0

x^{\frac{4}{3}} 3 x^{2} - x - 20 = 0

Calculate

x^{2} - x - 20 = 0

Factor the expression

More Steps

(x - 5) (x + 4) = 0

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

x - 5 = 0 x + 4 = 0

Solve the equation for x

More Steps

x = 5 x + 4 = 0

Solve the equation for x

More Steps

x = 5 x = - 4

Check if the solution is in the defined range

x = 5 x = - 4, x \neq = 0

Find the intersection of the solution and the defined range

x = 5 x = - 4

Solution

x_{1} = - 4, x_{2} = 5

Show Solution