Solve f^4 1963-4-17

Question

Simplify the expression

1963 f^{4} - 21

Evaluate

f^{4} \times 1963 - 4 - 17

Use the commutative property to reorder the terms

1963 f^{4} - 4 - 17

Solution

1963 f^{4} - 21

Show Solution

f_{1} = - \frac{4 21 \times 196 3 ^{3}}{1963}, f_{2} = \frac{4 21 \times 196 3 ^{3}}{1963}

Alternative Form

f_{1} \approx - 0.321606, f_{2} \approx 0.321606

Evaluate

f^{4} \times 1963 - 4 - 17

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

f^{4} \times 1963 - 4 - 17 = 0

Use the commutative property to reorder the terms

1963 f^{4} - 4 - 17 = 0

Subtract the numbers

1963 f^{4} - 21 = 0

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

1963 f^{4} = 0 + 21

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

1963 f^{4} = 21

Divide both sides

\frac{1963 f ^{4}}{1963} = \frac{21}{1963}

Divide the numbers

f^{4} = \frac{21}{1963}

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

f = \pm 4 \frac{21}{1963}

Simplify the expression

More Steps

Evaluate

4 \frac{21}{1963}

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

\frac{4 21}{4 1963}

Multiply by the Conjugate

\frac{4 21 \times 4 196 3 ^{3}}{4 1963 \times 4 196 3 ^{3}}

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

\frac{4 21 \times 196 3 ^{3}}{4 1963 \times 4 196 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

41963 \times 4 196 3^{3}

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

4 1963 \times 196 3^{3}

Calculate the product

4 196 3^{4}

Reduce the index of the radical and exponent with 4

1963

\frac{4 21 \times 196 3 ^{3}}{1963}

f = \pm \frac{4 21 \times 196 3 ^{3}}{1963}

Separate the equation into 2 possible cases

f = \frac{4 21 \times 196 3 ^{3}}{1963} f = - \frac{4 21 \times 196 3 ^{3}}{1963}

Solution

f_{1} = - \frac{4 21 \times 196 3 ^{3}}{1963}, f_{2} = \frac{4 21 \times 196 3 ^{3}}{1963}

Alternative Form

f_{1} \approx - 0.321606, f_{2} \approx 0.321606

Show Solution