Solve 3r^2-3r^4=10r

Evaluate

3 r^{2} - 3 r^{4} = 10 r

Rewrite the expression

3 r^{2} - 3 r^{4} - 10 r = 0

Use substitution

More Steps

3 x^{2} + 3 y^{2} - 3 x^{4} - 6 x^{2} y^{2} - 3 y^{4} - 10 r = 0

Simplify the expression

- 10 r = - 3 x^{2} - 3 y^{2} + 3 x^{4} + 6 x^{2} y^{2} + 3 y^{4}

Square both sides of the equation

(- 10 r)^{2} = (- 3 x^{2} - 3 y^{2} + 3 x^{4} + 6 x^{2} y^{2} + 3 y^{4})^{2}

Evaluate

100 r^{2} = (- 3 x^{2} - 3 y^{2} + 3 x^{4} + 6 x^{2} y^{2} + 3 y^{4})^{2}

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

100 (x^{2} + y^{2}) = (- 3 x^{2} - 3 y^{2} + 3 x^{4} + 6 x^{2} y^{2} + 3 y^{4})^{2}

Solution

100 x^{2} + 100 y^{2} = 9 x^{4} + 18 x^{2} y^{2} - 18 x^{6} - 54 x^{4} y^{2} - 54 x^{2} y^{4} + 9 y^{4} - 18 y^{6} + 9 x^{8} + 36 x^{6} y^{2} + 54 x^{4} y^{4} + 36 x^{2} y^{6} + 9 y^{8}

3r^2 3r^4=10r