Solve (x^(2 ) 6x^5)⋅ root(2)(x^3)>0

Evaluate

(x^{2} \times 6 x^{5}) x^{3} > 0

Find the domain

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(x^{2} \times 6 x^{5}) x^{3} > 0, x \geq 0

Remove the parentheses

x^{2} \times 6 x^{5} x^{3} > 0

Multiply

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6 x^{7} x^{3} > 0

Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when 6 x^{7} x^{3} = 0

6 x^{7} x^{3} = 0

Elimination the left coefficient

x^{7} x^{3} = 0

Separate the equation into 2 possible cases

x^{7} = 0 x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0 x^{3} = 0

Solve the equation

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x = 0 x = 0

Find the union

x = 0

Exclude the impossible values of x

x \neq = 0

Check if the solution is in the defined range

x \neq = 0, x \geq 0

Solution

x > 0

Alternative Form

x \in (0, + \infty)

Solve the inequality