Solve e = e1r^2 e^2r1

Question

Solve the equation

r = \frac{3 e}{e}

Alternative Form

r \approx 0.513417

Evaluate

e = e \times 1 \times r^{2} e^{2} r \times 1

Multiply the terms

More Steps

Evaluate

e \times 1 \times r^{2} e^{2} r \times 1

Rewrite the expression

e r^{2} e^{2} r

Multiply the terms with the same base by adding their exponents

e^{1 + 2} r^{2} \times r

Add the numbers

e^{3} r^{2} \times r

Multiply the terms with the same base by adding their exponents

e^{3} r^{2 + 1}

Add the numbers

e^{3} r^{3}

e = e^{3} r^{3}

Swap the sides of the equation

e^{3} r^{3} = e

Divide both sides

\frac{e ^{3} r ^{3}}{e ^{3}} = \frac{e}{e ^{3}}

Divide the numbers

r^{3} = \frac{e}{e ^{3}}

Divide the numbers

r^{3} = \frac{1}{e ^{2}}

Take the 3 -th root on both sides of the equation

3 r^{3} = 3 \frac{1}{e ^{2}}

Calculate

r = 3 \frac{1}{e ^{2}}

Solution

More Steps

Evaluate

3 \frac{1}{e ^{2}}

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

\frac{3 1}{3 e ^{2}}

Simplify the radical expression

\frac{1}{3 e ^{2}}

Multiply by the Conjugate

\frac{3 e}{3 e ^{2} \times 3 e}

Multiply the numbers

More Steps

Evaluate

3 e^{2} \times 3 e

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

3 e^{2} \times e

Calculate the product

3 e^{3}

Reduce the index of the radical and exponent with 3

e

\frac{3 e}{e}

r = \frac{3 e}{e}

Alternative Form

r \approx 0.513417

Show Solution

Rewrite the equation

e^{4} x^{6} + 3 e^{4} x^{4} y^{2} + 3 e^{4} x^{2} y^{4} + e^{4} y^{6} = 1

Evaluate

e = e \times 1 \times r^{2} e^{2} r \times 1

Evaluate

More Steps

Evaluate

e \times 1 \times r^{2} e^{2} r \times 1

Rewrite the expression

e r^{2} e^{2} r

Multiply the terms with the same base by adding their exponents

e^{1 + 2} r^{2} \times r

Add the numbers

e^{3} r^{2} \times r

Multiply the terms with the same base by adding their exponents

e^{3} r^{2 + 1}

Add the numbers

e^{3} r^{3}

e = e^{3} r^{3}

Rewrite the expression

- e^{3} r^{3} = - e

Divide both sides of the equation by - e

e^{2} r^{3} = 1

Evaluate

e^{2} r^{2} \times r = 1

Evaluate

e^{2} (x^{2} + y^{2}) r = 1

Square both sides of the equation

(e^{2} (x^{2} + y^{2}) r)^{2} = 1^{2}

Evaluate

(e^{2} (x^{2} + y^{2}))^{2} r^{2} = 1^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

(e^{2} (x^{2} + y^{2}))^{2} (x^{2} + y^{2}) = 1^{2}

Use substitution

(e^{4} x^{4} + 2 e^{4} x^{2} y^{2} + e^{4} y^{4}) (x^{2} + y^{2}) = 1^{2}

Evaluate the power

(e^{4} x^{4} + 2 e^{4} x^{2} y^{2} + e^{4} y^{4}) (x^{2} + y^{2}) = 1

Solution

e^{4} x^{6} + 3 e^{4} x^{4} y^{2} + 3 e^{4} x^{2} y^{4} + e^{4} y^{6} = 1

Show Solution

Solve the equation

Rewrite the equation

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