Solve 2917r=583r^2r^5

Question

Solve the equation

r_{1} = - \frac{6 2917 \times 58 3 ^{5}}{583}, r_{2} = 0, r_{3} = \frac{6 2917 \times 58 3 ^{5}}{583}

Alternative Form

r_{1} \approx - 1.30781, r_{2} = 0, r_{3} \approx 1.30781

Evaluate

2917 r = 583 r^{2} \times r^{5}

Multiply

More Steps

Evaluate

583 r^{2} \times r^{5}

Multiply the terms with the same base by adding their exponents

583 r^{2 + 5}

Add the numbers

583 r^{7}

2917 r = 583 r^{7}

Add or subtract both sides

2917 r - 583 r^{7} = 0

Factor the expression

r (2917 - 583 r^{6}) = 0

Separate the equation into 2 possible cases

r = 0 2917 - 583 r^{6} = 0

Solve the equation

More Steps

Evaluate

2917 - 583 r^{6} = 0

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

- 583 r^{6} = 0 - 2917

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

- 583 r^{6} = - 2917

Change the signs on both sides of the equation

583 r^{6} = 2917

Divide both sides

\frac{583 r ^{6}}{583} = \frac{2917}{583}

Divide the numbers

r^{6} = \frac{2917}{583}

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

r = \pm 6 \frac{2917}{583}

Simplify the expression

More Steps

Evaluate

6 \frac{2917}{583}

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

\frac{6 2917}{6 583}

Multiply by the Conjugate

\frac{6 2917 \times 6 58 3 ^{5}}{6 583 \times 6 58 3 ^{5}}

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

\frac{6 2917 \times 58 3 ^{5}}{6 583 \times 6 58 3 ^{5}}

Multiply the numbers

\frac{6 2917 \times 58 3 ^{5}}{583}

r = \pm \frac{6 2917 \times 58 3 ^{5}}{583}

Separate the equation into 2 possible cases

r = \frac{6 2917 \times 58 3 ^{5}}{583} r = - \frac{6 2917 \times 58 3 ^{5}}{583}

r = 0 r = \frac{6 2917 \times 58 3 ^{5}}{583} r = - \frac{6 2917 \times 58 3 ^{5}}{583}

Solution

r_{1} = - \frac{6 2917 \times 58 3 ^{5}}{583}, r_{2} = 0, r_{3} = \frac{6 2917 \times 58 3 ^{5}}{583}

Alternative Form

r_{1} \approx - 1.30781, r_{2} = 0, r_{3} \approx 1.30781

Show Solution

58 3^{2} x^{14} + 58 3^{2} x^{12} y^{2} + 2039334 x^{12} y^{2} + 4078668 x^{10} y^{4} + 8837114 x^{8} y^{6} + 8837114 x^{6} y^{8} - 3401222 x^{8} - 13604888 x^{6} y^{2} + 174 9^{2} x^{10} y^{4} + 174 9^{2} x^{8} y^{6} + 4078668 x^{4} y^{10} - 20407332 x^{4} y^{4} + 174 9^{2} x^{6} y^{8} + 174 9^{2} x^{4} y^{10} + 2039334 x^{2} y^{12} - 13604888 x^{2} y^{6} + 58 3^{2} y^{12} x^{2} + 58 3^{2} y^{14} - 3401222 y^{8} + 291 7^{2} x^{2} + 291 7^{2} y^{2} = 0

Evaluate

2917 r = 583 r^{2} \times r^{5}

Evaluate

More Steps

Evaluate

583 r^{2} \times r^{5}

Multiply the terms with the same base by adding their exponents

583 r^{2 + 5}

Add the numbers

583 r^{7}

2917 r = 583 r^{7}

Rewrite the expression

2917 r - 583 r^{7} = 0

Evaluate

(- 583 r^{6} + 2917) r = 0

Evaluate

(- 583 x^{6} - 1749 x^{4} y^{2} - 1749 x^{2} y^{4} - 583 y^{6} + 2917) r = 0

Square both sides of the equation

((- 583 x^{6} - 1749 x^{4} y^{2} - 1749 x^{2} y^{4} - 583 y^{6} + 2917) r)^{2} = 0

Evaluate

(- 583 x^{6} - 1749 x^{4} y^{2} - 1749 x^{2} y^{4} - 583 y^{6} + 2917)^{2} r^{2} = 0

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

(- 583 x^{6} - 1749 x^{4} y^{2} - 1749 x^{2} y^{4} - 583 y^{6} + 2917)^{2} (x^{2} + y^{2}) = 0

Solution

58 3^{2} x^{14} + 58 3^{2} x^{12} y^{2} + 2039334 x^{12} y^{2} + 4078668 x^{10} y^{4} + 8837114 x^{8} y^{6} + 8837114 x^{6} y^{8} - 3401222 x^{8} - 13604888 x^{6} y^{2} + 174 9^{2} x^{10} y^{4} + 174 9^{2} x^{8} y^{6} + 4078668 x^{4} y^{10} - 20407332 x^{4} y^{4} + 174 9^{2} x^{6} y^{8} + 174 9^{2} x^{4} y^{10} + 2039334 x^{2} y^{12} - 13604888 x^{2} y^{6} + 58 3^{2} y^{12} x^{2} + 58 3^{2} y^{14} - 3401222 y^{8} + 291 7^{2} x^{2} + 291 7^{2} y^{2} = 0

Show Solution