Solve u* u^38 = 12

Question

Solve the equation

u_{1} = - \frac{4 24}{2}, u_{2} = \frac{4 24}{2}

Alternative Form

u_{1} \approx - 1.106682, u_{2} \approx 1.106682

Evaluate

u \times u^{3} \times 8 = 12

Multiply

More Steps

Evaluate

u \times u^{3} \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} = 12

Divide both sides

\frac{8 u ^{4}}{8} = \frac{12}{8}

Divide the numbers

u^{4} = \frac{12}{8}

Cancel out the common factor 4

u^{4} = \frac{3}{2}

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

u = \pm 4 \frac{3}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{2}

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

\frac{4 3}{4 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

43 \times 48

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

4 3 \times 8

Calculate the product

424

\frac{4 24}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 24}{2}

u = \pm \frac{4 24}{2}

Separate the equation into 2 possible cases

u = \frac{4 24}{2} u = - \frac{4 24}{2}

Solution

u_{1} = - \frac{4 24}{2}, u_{2} = \frac{4 24}{2}

Alternative Form

u_{1} \approx - 1.106682, u_{2} \approx 1.106682

Show Solution