Solve a^2-25/a^3 * 1/a^2 5a

Question

Simplify the expression

\frac{a ^{6} - 125}{a ^{4}}

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a = 0

Show Solution

a_{1} = - 5, a_{2} = 5

Alternative Form

a_{1} \approx - 2.236068, a_{2} \approx 2.236068

Evaluate

a^{2} - \frac{25}{a ^{3}} \times \frac{1}{a ^{2}} \times 5 a

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

a^{2} - \frac{25}{a ^{3}} \times \frac{1}{a ^{2}} \times 5 a = 0

Find the domain

More Steps

a^{2} - \frac{25}{a ^{3}} \times \frac{1}{a ^{2}} \times 5 a = 0, a \neq = 0

Calculate

a^{2} - \frac{25}{a ^{3}} \times \frac{1}{a ^{2}} \times 5 a = 0

Multiply the terms

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a^{2} - \frac{125}{a ^{4}} = 0

Subtract the terms

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\frac{a ^{6} - 125}{a ^{4}} = 0

Cross multiply

a^{6} - 125 = a^{4} \times 0

Simplify the equation

a^{6} - 125 = 0

Move the constant to the right side

a^{6} = 125

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

a = \pm 6125

Simplify the expression

More Steps

a = \pm 5

Separate the equation into 2 possible cases

a = 5 a = - 5

Check if the solution is in the defined range

a = 5 a = - 5, a \neq = 0

Find the intersection of the solution and the defined range

a = 5 a = - 5

Solution

a_{1} = - 5, a_{2} = 5

Alternative Form

a_{1} \approx - 2.236068, a_{2} \approx 2.236068

Show Solution