Divide $x^{6} - y^{6}$ by the product of $x^{2} + x y + y^{2} a n d x - y$ .

Open in App

Solution

$P r o d u c t o f (x^{2} + x y + y^{2}) a n d (x - y) = (x - y) (x^{2} + x y + y^{2}) = x (x^{2} + x y + y^{2}) - y (x^{2} + x y + y^{2}) = x^{3} + x^{2} y + x y^{2} - x^{2} y - x y^{2} - y^{3} = x^{3} - y^{3} N o w, (x^{6} - y^{6}) \div (x^{3} - y^{3}) = x^{3} + y^{3} x^{3} - y^{3}) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ x^{6} - y^{6} (x^{3} + y^{3} x^{6} - x^{3} y^{3} - + - ------------- - x^{3} y^{3} - y^{6} x^{3} y^{3} - y^{6} - + - -------- - \times - -------- -$

Suggest Corrections

Similar questions

\sqrt{1 - x^{6}} + \sqrt{1 - y^{6}} = a^{3} (x^{3} - y^{3})

\frac{d y}{d x} = \frac{x^{2}}{y^{2}} \sqrt{\frac{1 - y^{6}}{1 - x^{6}}}

Factors of $x^{6} - y^{6}$ is:

\sqrt{1 - x^{6}} + \sqrt{1 - y^{6}} = a^{3} . (x^{3} - y^{3})

\frac{d y}{d x} = \frac{x^{2}}{y^{2}} \sqrt{\frac{1 - y^{6}}{1 - x^{6}}}

\frac{x^{2} - x y}{y^{2} - x y}

\frac{x}{y}

\sqrt{1 - x^{6}} + \sqrt{1 - y^{6}} = a (x^{3} - y^{3})

\frac{d y}{d x} = f (x, y) \sqrt{\frac{1 - y^{6}}{1 - x^{6}}}

Join BYJU'S Learning Program