Question

x/y+y/x=-1 then prove x³-y³

Answer 1

Answer:

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Answer 2

Answer:

We are given that:

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