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

Evaluate

x^{(- 1) \div 2} (x^{5 \div 2} - 2 x^{3 \div 3})

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

x^{(- 1) \div 2} (x^{5 \div 2} - 2 x^{3 \div 3}) = 0

Find the domain

x^{(- 1) \div 2} (x^{5 \div 2} - 2 x^{3 \div 3}) = 0, x > 0

Calculate

x^{(- 1) \div 2} (x^{5 \div 2} - 2 x^{3 \div 3}) = 0

Divide the numbers

x^{(- 1) \div 2} (x^{5 \div 2} - 2 x^{1}) = 0

Divide the numbers

x^{(- 1) \div 2} (x^{2.5} - 2 x^{1}) = 0

Evaluate the power

x^{(- 1) \div 2} (x^{2.5} - 2 x) = 0

Convert the decimal into a fraction

More Steps

x^{(- 1) \div 2} (x^{\frac{5}{2}} - 2 x) = 0

Divide the numbers

x^{- 0.5} (x^{\frac{5}{2}} - 2 x) = 0

Convert the decimal into a fraction

More Steps

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

x \in \emptyset x^{\frac{5}{2}} - 2 x = 0

Solve the equation

More Steps

x \in \emptyset x = 0 x = 34

Find the union

x = 0 x = 34

Check if the solution is in the defined range

x = 0 x = 34, x > 0

Solution

x = 34

Alternative Form

x \approx 1.587401

Simplify the expression