Solve 2a^517a-2 - Socratic AI (ScanMath)

Вопрос

Simplify the expression

34 a^{6} - 2

Evaluate

2 a^{5} \times 17 a - 2

Решение

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Evaluate

2 a^{5} \times 17 a

Multiply the terms

34 a^{5} \times a

Multiply the terms with the same base by adding their exponents

34 a^{5 + 1}

Add the numbers

34 a^{6}

34 a^{6} - 2

Показать решение

Factor the expression

2 (17 a^{6} - 1)

Evaluate

2 a^{5} \times 17 a - 2

Multiply

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Evaluate

2 a^{5} \times 17 a

Multiply the terms

34 a^{5} \times a

Multiply the terms with the same base by adding their exponents

34 a^{5 + 1}

Add the numbers

34 a^{6}

34 a^{6} - 2

Решение

2 (17 a^{6} - 1)

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Find the roots

a_{1} = - \frac{6 1 7 ^{5}}{17}, a_{2} = \frac{6 1 7 ^{5}}{17}

Alternative Form

a_{1} \approx - 0.623627, a_{2} \approx 0.623627

Evaluate

2 a^{5} \times 17 a - 2

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

2 a^{5} \times 17 a - 2 = 0

Multiply

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Multiply the terms

2 a^{5} \times 17 a

Multiply the terms

34 a^{5} \times a

Multiply the terms with the same base by adding their exponents

34 a^{5 + 1}

Add the numbers

34 a^{6}

34 a^{6} - 2 = 0

Move the constant to the right-hand side and change its sign

34 a^{6} = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

34 a^{6} = 2

Divide both sides

\frac{34 a ^{6}}{34} = \frac{2}{34}

Divide the numbers

a^{6} = \frac{2}{34}

Cancel out the common factor 2

a^{6} = \frac{1}{17}

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

a = \pm 6 \frac{1}{17}

Simplify the expression

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Evaluate

6 \frac{1}{17}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 1}{6 17}

Simplify the radical expression

\frac{1}{6 17}

Multiply by the Conjugate

\frac{6 1 7 ^{5}}{6 17 \times 6 1 7 ^{5}}

Multiply the numbers

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Evaluate

617 \times 6 1 7^{5}

The product of roots with the same index is equal to the root of the product

6 17 \times 1 7^{5}

Calculate the product

6 1 7^{6}

Reduce the index of the radical and exponent with 6

17

\frac{6 1 7 ^{5}}{17}

a = \pm \frac{6 1 7 ^{5}}{17}

Separate the equation into 2 possible cases

a = \frac{6 1 7 ^{5}}{17} a = - \frac{6 1 7 ^{5}}{17}

Решение

a_{1} = - \frac{6 1 7 ^{5}}{17}, a_{2} = \frac{6 1 7 ^{5}}{17}

Alternative Form

a_{1} \approx - 0.623627, a_{2} \approx 0.623627

Показать решение

2a^517a 2

Simplify the expression

Factor the expression

Find the roots