Solve l^2-2000 l^6307

Question

Simplify the expression

l^{2} - 614000 l^{6}

Evaluate

l^{2} - 2000 l^{6} \times 307

Solution

l^{2} - 614000 l^{6}

Show Solution

l^{2} (1 - 614000 l^{4})

Evaluate

l^{2} - 2000 l^{6} \times 307

Multiply the terms

l^{2} - 614000 l^{6}

Rewrite the expression

l^{2} - l^{2} \times 614000 l^{4}

Solution

l^{2} (1 - 614000 l^{4})

Show Solution

l_{1} = - \frac{4 3837 5 ^{3}}{76750}, l_{2} = 0, l_{3} = \frac{4 3837 5 ^{3}}{76750}

Alternative Form

l_{1} \approx - 0.035724, l_{2} = 0, l_{3} \approx 0.035724

Evaluate

l^{2} - 2000 l^{6} \times 307

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

l^{2} - 2000 l^{6} \times 307 = 0

Multiply the terms

l^{2} - 614000 l^{6} = 0

Factor the expression

l^{2} (1 - 614000 l^{4}) = 0

Separate the equation into 2 possible cases

l^{2} = 0 1 - 614000 l^{4} = 0

The only way a power can be 0 is when the base equals 0

l = 0 1 - 614000 l^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 614000 l^{4} = 0

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

- 614000 l^{4} = 0 - 1

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

- 614000 l^{4} = - 1

Change the signs on both sides of the equation

614000 l^{4} = 1

Divide both sides

\frac{614000 l ^{4}}{614000} = \frac{1}{614000}

Divide the numbers

l^{4} = \frac{1}{614000}

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

l = \pm 4 \frac{1}{614000}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{614000}

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

\frac{4 1}{4 614000}

Simplify the radical expression

\frac{1}{4 614000}

Simplify the radical expression

\frac{1}{2 4 38375}

Multiply by the Conjugate

\frac{4 3837 5 ^{3}}{2 4 38375 \times 4 3837 5 ^{3}}

Multiply the numbers

\frac{4 3837 5 ^{3}}{76750}

l = \pm \frac{4 3837 5 ^{3}}{76750}

Separate the equation into 2 possible cases

l = \frac{4 3837 5 ^{3}}{76750} l = - \frac{4 3837 5 ^{3}}{76750}

l = 0 l = \frac{4 3837 5 ^{3}}{76750} l = - \frac{4 3837 5 ^{3}}{76750}

Solution

l_{1} = - \frac{4 3837 5 ^{3}}{76750}, l_{2} = 0, l_{3} = \frac{4 3837 5 ^{3}}{76750}

Alternative Form

l_{1} \approx - 0.035724, l_{2} = 0, l_{3} \approx 0.035724

Show Solution