Solve - 2/3 a^5/6 a- 1/6

Question

Simplify the expression

- \frac{2 a ^{6} + 3}{18}

Show Solution

a_{1} = - \frac{6 2592}{4} - \frac{6 96}{4} i, a_{2} = \frac{6 2592}{4} + \frac{6 96}{4} i

Alternative Form

a_{1} \approx - 0.926572 - 0.534957 i, a_{2} \approx 0.926572 + 0.534957 i

Evaluate

- \frac{2}{3} \times \frac{a ^{5}}{6} a - \frac{1}{6}

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

- \frac{2}{3} \times \frac{a ^{5}}{6} a - \frac{1}{6} = 0

Multiply the terms

More Steps

- \frac{a ^{6}}{9} - \frac{1}{6} = 0

Subtract the terms

More Steps

- \frac{2 a ^{6} + 3}{18} = 0

Simplify

- 2 a^{6} - 3 = 0

Move the constant to the right side

- 2 a^{6} = 3

Change the signs on both sides of the equation

2 a^{6} = - 3

Divide both sides

\frac{2 a ^{6}}{2} = \frac{- 3}{2}

Divide the numbers

a^{6} = \frac{- 3}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

a^{6} = - \frac{3}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm 6 - \frac{3}{2}

Simplify the expression

More Steps

a = \pm (\frac{6 2592}{4} + \frac{6 96}{4} i)

Separate the equation into 2 possible cases

a = \frac{6 2592}{4} + \frac{6 96}{4} i a = - \frac{6 2592}{4} - \frac{6 96}{4} i

Solution

a_{1} = - \frac{6 2592}{4} - \frac{6 96}{4} i, a_{2} = \frac{6 2592}{4} + \frac{6 96}{4} i

Alternative Form

a_{1} \approx - 0.926572 - 0.534957 i, a_{2} \approx 0.926572 + 0.534957 i

Show Solution