Solve 4a+85a-20/a^2-3a-10a^2-4a

Question

Simplify the expression

\frac{82 a ^{3} - 20 - 10 a ^{4}}{a ^{2}}

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a = 0

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a_{1} \approx 0.642009, a_{2} \approx 8.196368

Evaluate

4 a + 85 a - \frac{20}{a ^{2}} - 3 a - 10 a^{2} - 4 a

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

4 a + 85 a - \frac{20}{a ^{2}} - 3 a - 10 a^{2} - 4 a = 0

The only way a power can not be 0 is when the base not equals 0

4 a + 85 a - \frac{20}{a ^{2}} - 3 a - 10 a^{2} - 4 a = 0, a \neq = 0

Calculate

4 a + 85 a - \frac{20}{a ^{2}} - 3 a - 10 a^{2} - 4 a = 0

Add the terms

More Steps

89 a - \frac{20}{a ^{2}} - 3 a - 10 a^{2} - 4 a = 0

Subtract the terms

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\frac{89 a ^{3} - 20}{a ^{2}} - 3 a - 10 a^{2} - 4 a = 0

Subtract the terms

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\frac{86 a ^{3} - 20}{a ^{2}} - 10 a^{2} - 4 a = 0

Subtract the terms

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\frac{86 a ^{3} - 20 - 10 a ^{4}}{a ^{2}} - 4 a = 0

Subtract the terms

More Steps

\frac{82 a ^{3} - 20 - 10 a ^{4}}{a ^{2}} = 0

Cross multiply

82 a^{3} - 20 - 10 a^{4} = a^{2} \times 0

Simplify the equation

82 a^{3} - 20 - 10 a^{4} = 0

Factor the expression

2 (41 a^{3} - 10 - 5 a^{4}) = 0

Divide both sides

41 a^{3} - 10 - 5 a^{4} = 0

Calculate

a \approx 0.642009 a \approx 8.196368

Check if the solution is in the defined range

a \approx 0.642009 a \approx 8.196368, a \neq = 0

Find the intersection of the solution and the defined range

a \approx 0.642009 a \approx 8.196368

Solution

a_{1} \approx 0.642009, a_{2} \approx 8.196368

Show Solution