Question

If X square + Y square is equals to 4 and x minus y is equals to 3 then find the value of x cube minus y cube

Answer 1

Answer:

$\frac{9}{2}$

Step-by-step explanation:

We are given the values:

$X^{2} +Y^{2} =4$ ... (1) and

$X-Y=3$ .... (2)

We have to find the value of $(X^{3} -Y^{3} )$

Now we will calculate it.

Squaring both sides of equation (2), we get

$X^{2}-2XY+Y^{2}=9$

⇒$-2XY+(X^{2}+Y^{2})=9$

⇒$-2XY+4=9$  [From equation (1)]

⇒$-2XY=5$

⇒$XY=-\frac{5}{2}$ ...... (3)

Now, we have the formula

$(X^{3}-Y^{3})=(X-Y)(X^{2}+XY+Y^{2}  )$

Using equations (1) and (2)

⇒$(X^{3}-Y^{3})=(3)(4-\frac{5}{2})$

⇒$(X^{3}-Y^{3})=(3)(\frac{3}{2})$

⇒$(X^{3}-Y^{3})=\frac{9}{2}$ (Answer)