Solve 135/a^2-6a*a-6/3a 9-5a/a^3

Question

Simplify the expression

\frac{130 - 6 a ^{4} - 18 a ^{3}}{a ^{2}}

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a = 0

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a_{1} \approx - 3.503732, a_{2} \approx 1.668084

Evaluate

\frac{135}{a ^{2}} - 6 a \times a - \frac{6}{3} a \times 9 - (5 \times \frac{a}{a ^{3}})

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

\frac{135}{a ^{2}} - 6 a \times a - \frac{6}{3} a \times 9 - (5 \times \frac{a}{a ^{3}}) = 0

Find the domain

More Steps

\frac{135}{a ^{2}} - 6 a \times a - \frac{6}{3} a \times 9 - (5 \times \frac{a}{a ^{3}}) = 0, a \neq = 0

Calculate

\frac{135}{a ^{2}} - 6 a \times a - \frac{6}{3} a \times 9 - (5 \times \frac{a}{a ^{3}}) = 0

Divide the terms

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\frac{135}{a ^{2}} - 6 a \times a - \frac{6}{3} a \times 9 - (5 \times \frac{1}{a ^{2}}) = 0

Multiply the terms

\frac{135}{a ^{2}} - 6 a \times a - \frac{6}{3} a \times 9 - \frac{5}{a ^{2}} = 0

Multiply the terms

\frac{135}{a ^{2}} - 6 a^{2} - \frac{6}{3} a \times 9 - \frac{5}{a ^{2}} = 0

Divide the terms

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\frac{135}{a ^{2}} - 6 a^{2} - 2 a \times 9 - \frac{5}{a ^{2}} = 0

Multiply the terms

\frac{135}{a ^{2}} - 6 a^{2} - 18 a - \frac{5}{a ^{2}} = 0

Subtract the terms

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\frac{135 - 6 a ^{4}}{a ^{2}} - 18 a - \frac{5}{a ^{2}} = 0

Subtract the terms

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\frac{135 - 6 a ^{4} - 18 a ^{3}}{a ^{2}} - \frac{5}{a ^{2}} = 0

Subtract the terms

More Steps

\frac{130 - 6 a ^{4} - 18 a ^{3}}{a ^{2}} = 0

Cross multiply

130 - 6 a^{4} - 18 a^{3} = a^{2} \times 0

Simplify the equation

130 - 6 a^{4} - 18 a^{3} = 0

Factor the expression

2 (65 - 3 a^{4} - 9 a^{3}) = 0

Divide both sides

65 - 3 a^{4} - 9 a^{3} = 0

Calculate

a \approx - 3.503732 a \approx 1.668084

Check if the solution is in the defined range

a \approx - 3.503732 a \approx 1.668084, a \neq = 0

Find the intersection of the solution and the defined range

a \approx - 3.503732 a \approx 1.668084

Solution

a_{1} \approx - 3.503732, a_{2} \approx 1.668084

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