Solve u1 u8 u^21 = 117

Question

Solve the equation

u_{1} = - \frac{4 234}{2}, u_{2} = \frac{4 234}{2}

Alternative Form

u_{1} \approx - 1.955573, u_{2} \approx 1.955573

Evaluate

u \times 1 \times u \times 8 u^{2} \times 1 = 117

Multiply the terms

More Steps

Evaluate

u \times 1 \times u \times 8 u^{2} \times 1

Rewrite the expression

u \times u \times 8 u^{2}

Multiply the terms with the same base by adding their exponents

u^{1 + 2} \times u \times 8

Add the numbers

u^{3} \times u \times 8

Multiply the terms with the same base by adding their exponents

u^{1 + 3} \times 8

Add the numbers

u^{4} \times 8

Use the commutative property to reorder the terms

8 u^{4}

8 u^{4} = 117

Divide both sides

\frac{8 u ^{4}}{8} = \frac{117}{8}

Divide the numbers

u^{4} = \frac{117}{8}

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

u = \pm 4 \frac{117}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{117}{8}

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

\frac{4 117}{4 8}

Multiply by the Conjugate

\frac{4 117 \times 4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{4 117 \times 2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

4117 \times 2^{2} 42

Multiply the terms

4234 \times 2^{2}

Use the commutative property to reorder the terms

2^{2} 4234

\frac{2 ^{2} 4 234}{4 8 \times 4 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 4 8^{3}

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

4 8 \times 8^{3}

Calculate the product

4 8^{4}

Transform the expression

4 2^{12}

Reduce the index of the radical and exponent with 4

2^{3}

\frac{2 ^{2} 4 234}{2 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{2}}{2 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{3 - 2}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{4 234}{2}

u = \pm \frac{4 234}{2}

Separate the equation into 2 possible cases

u = \frac{4 234}{2} u = - \frac{4 234}{2}

Solution

u_{1} = - \frac{4 234}{2}, u_{2} = \frac{4 234}{2}

Alternative Form

u_{1} \approx - 1.955573, u_{2} \approx 1.955573

Show Solution