Solve 3x^(3/2) - 9x^(1/26)x^(-(1/2))

Question

Simplify the expression

\frac{3 x ^{2} x - 9 13 x ^{7}}{x}

Show Solution

x = 51 3^{26}

Alternative Form

x \approx 1.750807

Evaluate

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{26}} \times x^{- (\frac{1}{2})}

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

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{26}} \times x^{- (\frac{1}{2})} = 0

Find the domain

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{26}} \times x^{- (\frac{1}{2})} = 0, x > 0

Calculate

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{26}} \times x^{- (\frac{1}{2})} = 0

Remove the unnecessary parentheses

3 x^{\frac{3}{2}} - 9 x^{\frac{1}{26}} \times x^{- \frac{1}{2}} = 0

Multiply

More Steps

3 x^{\frac{3}{2}} - 9 x^{- \frac{6}{13}} = 0

Rewrite the expression

More Steps

3 x^{\frac{3}{2}} - \frac{9}{x ^{\frac{6}{13}}} = 0

Multiply both sides of the equation by LCD

(3 x^{\frac{3}{2}} - \frac{9}{x ^{\frac{6}{13}}}) x^{\frac{6}{13}} = 0 \times x^{\frac{6}{13}}

Simplify the equation

More Steps

3 x 26 x^{25} - 9 = 0 \times x^{\frac{6}{13}}

Any expression multiplied by 0 equals 0

3 x 26 x^{25} - 9 = 0

Move the constant to the right-hand side and change its sign

3 x 26 x^{25} = 9

Divide both sides of the equation by 3

x 26 x^{25} = 3

Raise both sides of the equation to the 26 -th power to eliminate the isolated 26 -th root

(x 26 x^{25})^{26} = 3^{26}

Evaluate the power

x^{51} = 3^{26}

Take the 51 -th root on both sides of the equation

51 x^{51} = 51 3^{26}

Calculate

x = 51 3^{26}

Check if the solution is in the defined range

x = 51 3^{26}, x > 0

Solution

x = 51 3^{26}

Alternative Form

x \approx 1.750807

Show Solution