If $(x^{3 / 2} - x y^{1 / 2} + x^{1 / 2} y - y^{3 / 2})$ is divided by $(x^{1 / 2} - y^{1 / 2})$ , the quotient is:

x + y

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

x - y

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

x^{1 / 2} - y^{1 / 2}

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

x^{2} - y^{2}

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

Open in App

Solution

The correct option is A $x + y$
$(x^{3 / 2} - x y^{1 / 2} + x^{1 / 2} y - y^{3 / 2})$ is divided by $(x^{1 / 2} - y^{1 / 2})$
$= x (x^{1 / 2} - y^{1 / 2}) + y (x^{1 / 2} - y^{1 / 2})$
$(x + y) (x^{1 / 2} - y^{1 / 2})$
$∴$ $(x^{3 / 2} - x y^{1 / 2} + x^{1 / 2} y - y^{3 / 2}) \div (x^{1 / 2} - y^{1 / 2})$
$= \frac{(x + y) (x^{1 / 2} - y^{1 / 2})}{(x^{1 / 2} - y^{1 / 2})} = (x + y)$

Suggest Corrections

Similar questions

(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0

The coordinates of the mid-point of the line segment joining two points P(X₁, y₁, z₁) and Q(x₂, y₂, z₂) are:

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

\frac{y_{2} - y_{3}}{x_{2} x_{3}} + \frac{y_{3} - y_{1}}{x_{3} x_{1}} + \frac{y_{1} - y_{2}}{x_{1} x_{2}} = 0

Find the centroid of the triangle with vertices A $(x_{1}, y_{1})$ , B $(x_{2}, y_{2})$ and C $(x_{3}, y_{3})$ .

Z^{2} = \frac{x^{1 / 2} + y^{1 / 2}}{x^{1 / 3} + y^{1 / 3}}

x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = ?

Join BYJU'S Learning Program