Question

if x/y+y/x=1, then what will be the value of x^3+y^3?​

Answer 1

Step-by-step explanation:

x/y+y/x=1…(1)

By (1) , x and y must be both nozero in order for the fractions x/y and y/x to be defined. Hence, we have

x/y+y/x=1=>x2+y2=xy…(2)

Now, by (2) and by the well - known identity of the sum of two cubes, we see that:

x3+y3=(x+y)(x2−xy+y2)=(x+y)[(x2+y2)−xy]=

(x+y)(xy−xy)=0

Answer 2

Answer:

$x³+y³=0$

Step-by-step explanation:

Given,

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

Now,

$→\frac{(x²+y²)}{xy}=1$

$→x²+y²-xy=0$

$→(x+y)(x²-xy+y²)=0(x+y)$

Now,

$→(x+y)(x²-xy+x²)=x³+x³$

$→x³+x³=0$

Hence,

$\boxed{x³+y³}=0$