Solve 2(a^2 1/a^2)-(a-1/a)-7

Question

Simplify the expression

\frac{- 5 a - a ^{2} + 1}{a}

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a = 0

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a_{1} = - \frac{5 + 29}{2}, a_{2} = \frac{- 5 + 29}{2}

Alternative Form

a_{1} \approx - 5.192582, a_{2} \approx 0.192582

Evaluate

2 (a^{2} \times \frac{1}{a ^{2}}) - (a - \frac{1}{a}) - 7

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

2 (a^{2} \times \frac{1}{a ^{2}}) - (a - \frac{1}{a}) - 7 = 0

Find the domain

More Steps

2 (a^{2} \times \frac{1}{a ^{2}}) - (a - \frac{1}{a}) - 7 = 0, a \neq = 0

Calculate

2 (a^{2} \times \frac{1}{a ^{2}}) - (a - \frac{1}{a}) - 7 = 0

Multiply the terms

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2 \times 1 - (a - \frac{1}{a}) - 7 = 0

Subtract the terms

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2 \times 1 - \frac{a ^{2} - 1}{a} - 7 = 0

Any expression multiplied by 1 remains the same

2 - \frac{a ^{2} - 1}{a} - 7 = 0

Subtract the terms

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\frac{2 a - a ^{2} + 1}{a} - 7 = 0

Subtract the terms

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\frac{- 5 a - a ^{2} + 1}{a} = 0

Cross multiply

- 5 a - a^{2} + 1 = a \times 0

Simplify the equation

- 5 a - a^{2} + 1 = 0

Rewrite in standard form

- a^{2} - 5 a + 1 = 0

Multiply both sides

a^{2} + 5 a - 1 = 0

Substitute a= 1,b= 5 and c= - 1 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{- 5 \pm 5 ^{2} - 4 ( - 1 )}{2}

Simplify the expression

More Steps

a = \frac{- 5 \pm 29}{2}

Separate the equation into 2 possible cases

a = \frac{- 5 + 29}{2} a = \frac{- 5 - 29}{2}

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

a = \frac{- 5 + 29}{2} a = - \frac{5 + 29}{2}

Check if the solution is in the defined range

a = \frac{- 5 + 29}{2} a = - \frac{5 + 29}{2}, a \neq = 0

Find the intersection of the solution and the defined range

a = \frac{- 5 + 29}{2} a = - \frac{5 + 29}{2}

Solution

a_{1} = - \frac{5 + 29}{2}, a_{2} = \frac{- 5 + 29}{2}

Alternative Form

a_{1} \approx - 5.192582, a_{2} \approx 0.192582

Show Solution