Question

if x-y=-6,xy=4 then find x^3-y^3

Answer 1

If x-y = -6, then (x-y)^2 = 36 x^2 + y^2 - 2xy = 36 x^2 + y^2 = 36-8 =28 Now, x^3 + y^3= (x-y)(x^2 + xy +y^2) = -6 × (28 + 4) = -6 × 32 = -182

Answer 2

As per the data given in the above question.

In the above question, it is given that,

The given data is $x-y=-6$ and xy=4

We have to find the value of $x^{3} -y^{3}$.

Thus, the value of the given equation as follow,

$\begin{array}{l}(\mathrm{x}-\mathrm{y})^{3}=\mathrm{x}^{3}-\mathrm{y}^{3}-3 \mathrm{x}^{2} \mathrm{y}+3 \mathrm{xy}^{2}=-216 \\=\mathrm{x}^{3}-\mathrm{y}^{3}-3 \mathrm{yx}(\mathrm{x}-\mathrm{y})=-216 \\\mathrm{x}^{3}-\mathrm{y}^{3}=-216+3(4)(-6) \\\mathrm{x}^{3}-\mathrm{y}^{3}=-288\end{array}$

Hence the value is -288.