If x-y-y-x-1 then find x3-y3

The correct option is C 0We know that, x³ y³=(x y)(x²+xy+y²) ........(1) Given that, x/y+y/x= 1 x²+y²/xy= 1 x²+y² = xy Adding xy on both sides, we get x² ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Expansion of (a-b)^3

If x/y+y/x=-1...

Question

If $\frac{x}{y} + \frac{y}{x} = - 1$ then find $x^{3} - y^{3}$

-1

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

0.0

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

Open in App

Solution

The correct option is D 0.0
We know that,
$x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2}) . . . . . . . . (i)$
Given that,
$\frac{x}{y} + \frac{y}{x} = - 1$

$\Rightarrow \frac{x^{2} + y^{2}}{x y} = - 1$

$\Rightarrow x ² + y ² = - x y$
Adding $x y$ on both sides, we get
$x^{2} + y^{2} + x y = 0 . . . . . . . . . . . (i i)$
on substituting eq.(ii) in eq.(i), we get
$x^{3} - y^{3} = (x - y) (0)$
$∴$ $x^{3} - y^{3} = 0$

Suggest Corrections

261

Similar questions

Q. If

\frac{x}{y} + \frac{y}{x} = 1; x^{3} + y^{3} = ?

If x+y=7 and x*y=12 find x³+y³

Q. If

x + y = 7, x y = 0

, then find

x^{3} + y^{3}

Q. If x + y = 2 and

\frac{1}{x} + \frac{1}{y} = 2

then the value of

x^{3} + y^{3}

Q. If

\frac{x}{y} + \frac{y}{x} = - 1, (x, y \neq 0)

, then value of

x^{3} - y^{3}

is:

Join BYJU'S Learning Program

If xy+yx=−1 then find x3−y3

The correct option is D 0.0We know that,x3−y3=(x−y)(x2+xy+y2)........(i) Given that, xy+yx=−1 ⇒x2+y2xy=−1 ⇒x²+y²=−xy Adding xy on both sides, we get x2+y2+xy=0...........(ii)on substituting eq.(ii) in eq.(i), we getx3−y3=(x−y)(0) ∴ x3−y3=0

If $\frac{x}{y} + \frac{y}{x} = - 1$ then find $x^{3} - y^{3}$