Solve 24-105/f^4 - ScanMath

Question

Simplify the expression

\frac{24 f ^{4} - 105}{f ^{4}}

Show Solution

f = 0

Show Solution

f_{1} = - \frac{4 70}{2}, f_{2} = \frac{4 70}{2}

Alternative Form

f_{1} \approx - 1.446254, f_{2} \approx 1.446254

Evaluate

24 - \frac{105}{f ^{4}}

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

24 - \frac{105}{f ^{4}} = 0

The only way a power can not be 0 is when the base not equals 0

24 - \frac{105}{f ^{4}} = 0, f \neq = 0

Calculate

24 - \frac{105}{f ^{4}} = 0

Subtract the terms

More Steps

\frac{24 f ^{4} - 105}{f ^{4}} = 0

Cross multiply

24 f^{4} - 105 = f^{4} \times 0

Simplify the equation

24 f^{4} - 105 = 0

Move the constant to the right side

24 f^{4} = 105

Divide both sides

\frac{24 f ^{4}}{24} = \frac{105}{24}

Divide the numbers

f^{4} = \frac{105}{24}

Cancel out the common factor 3

f^{4} = \frac{35}{8}

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

f = \pm 4 \frac{35}{8}

Simplify the expression

More Steps

f = \pm \frac{4 70}{2}

Separate the equation into 2 possible cases

f = \frac{4 70}{2} f = - \frac{4 70}{2}

Check if the solution is in the defined range

f = \frac{4 70}{2} f = - \frac{4 70}{2}, f \neq = 0

Find the intersection of the solution and the defined range

f = \frac{4 70}{2} f = - \frac{4 70}{2}

Solution

f_{1} = - \frac{4 70}{2}, f_{2} = \frac{4 70}{2}

Alternative Form

f_{1} \approx - 1.446254, f_{2} \approx 1.446254

Show Solution