Solve e^39-l^261 - ScanMath

Question

Simplify the expression

9 e^{3} - 61 l^{2}

Evaluate

e^{3} \times 9 - l^{2} \times 61

Multiply the numbers

9 e^{3} - l^{2} \times 61

Solution

9 e^{3} - 61 l^{2}

Show Solution

l_{1} = - \frac{3 e 61 e}{61}, l_{2} = \frac{3 e 61 e}{61}

Alternative Form

l_{1} \approx - 1.721464, l_{2} \approx 1.721464

Evaluate

e^{3} \times 9 - l^{2} \times 61

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

e^{3} \times 9 - l^{2} \times 61 = 0

Multiply the numbers

9 e^{3} - l^{2} \times 61 = 0

Use the commutative property to reorder the terms

9 e^{3} - 61 l^{2} = 0

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

- 61 l^{2} = 0 - 9 e^{3}

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

- 61 l^{2} = - 9 e^{3}

Change the signs on both sides of the equation

61 l^{2} = 9 e^{3}

Divide both sides

\frac{61 l ^{2}}{61} = \frac{9 e ^{3}}{61}

Divide the numbers

l^{2} = \frac{9 e ^{3}}{61}

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

l = \pm \frac{9 e ^{3}}{61}

Simplify the expression

More Steps

Evaluate

\frac{9 e ^{3}}{61}

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

\frac{9 e ^{3}}{61}

Simplify the radical expression

More Steps

Evaluate

9 e^{3}

Rewrite the expression

9 \times e^{3}

Simplify the root

3 e e

\frac{3 e e}{61}

Multiply by the Conjugate

\frac{3 e e \times 61}{61 \times 61}

Multiply the numbers

More Steps

Evaluate

e \times 61

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

e \times 61

Calculate the product

61 e

\frac{3 e 61 e}{61 \times 61}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3 e 61 e}{61}

l = \pm \frac{3 e 61 e}{61}

Separate the equation into 2 possible cases

l = \frac{3 e 61 e}{61} l = - \frac{3 e 61 e}{61}

Solution

l_{1} = - \frac{3 e 61 e}{61}, l_{2} = \frac{3 e 61 e}{61}

Alternative Form

l_{1} \approx - 1.721464, l_{2} \approx 1.721464

Show Solution