The equation $x^{3} + x^{2} y - x y^{2} = y^{3}$ represents

three real straight lines

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

lines in which two of them are perpendicular to each other

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

lines in which two of them are coincident

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A three real straight lines
B lines in which two of them are perpendicular to each other
C lines in which two of them are coincident
$x^{3} - y^{3} + x^{2} y - x y^{2} = 0$
$⟹ (x - y) (x^{2} + y^{2} + x y) + x y (x - y) = 0$
$⟹ (x - y) (x^{2} + y^{2} + 2 x y) = 0$
$⟹ (x - y) (x + y)^{2} = 0$
so roots are $x - y = 0, x + y = 0, x + y = 0$
$x - y = 0$ and $x + y = 0$ are perpendicular to each other and two of them are coincident.

Suggest Corrections

Similar questions

a x^{3} - 9 x^{2} y - x y^{2} + 4 y^{3} = 0

(a > 0)

a

x^{3} - y^{3} = 127, x^{2} y - x y^{2} = 42

x^{3} + x^{2} y - x y^{2} - y^{3} - x^{2} + y^{2} = 0

\frac{d y}{d x}

x^{3} + x^{2} y + x y^{2} + y^{3} = 81

u = \frac{y^{3}}{3} + 2 x - x^{2} y a n d v = x y^{2} - 2 y - \frac{x^{3}}{3}

Join BYJU'S Learning Program