Solve 7/8j^4=6 - ScanMath

Question

Solve the equation

j_{1} = - \frac{2 4 1029}{7}, j_{2} = \frac{2 4 1029}{7}

Alternative Form

j_{1} \approx - 1.618213, j_{2} \approx 1.618213

Evaluate

\frac{7}{8} j^{4} = 6

Multiply by the reciprocal

\frac{7}{8} j^{4} \times \frac{8}{7} = 6 \times \frac{8}{7}

Multiply

j^{4} = 6 \times \frac{8}{7}

Multiply

More Steps

Evaluate

6 \times \frac{8}{7}

Multiply the numbers

\frac{6 \times 8}{7}

Multiply the numbers

\frac{48}{7}

j^{4} = \frac{48}{7}

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

j = \pm 4 \frac{48}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{48}{7}

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

\frac{4 48}{4 7}

Simplify the radical expression

More Steps

Evaluate

448

Write the expression as a product where the root of one of the factors can be evaluated

4 16 \times 3

Write the number in exponential form with the base of 2

4 2^{4} \times 3

The root of a product is equal to the product of the roots of each factor

4 2^{4} \times 43

Reduce the index of the radical and exponent with 4

243

\frac{2 4 3}{4 7}

Multiply by the Conjugate

\frac{2 4 3 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{2 4 3 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4343

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

4 3 \times 343

Calculate the product

41029

\frac{2 4 1029}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

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

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{2 4 1029}{7}

j = \pm \frac{2 4 1029}{7}

Separate the equation into 2 possible cases

j = \frac{2 4 1029}{7} j = - \frac{2 4 1029}{7}

Solution

j_{1} = - \frac{2 4 1029}{7}, j_{2} = \frac{2 4 1029}{7}

Alternative Form

j_{1} \approx - 1.618213, j_{2} \approx 1.618213

Show Solution