Question

If * + Y=-1,(x, y 80), then find the value
ух
of x3 - y3.​

Answer 1

Step-by-step explanation:

if

y

x

+

x

y

=−1

simplifies to x

2

+xy+y

2

=0

as (x

3

−y

3

)=(x−y)(x

2

+xy+y

2

)=0 using above result

Answer 2

Answer:

The first thing one can note is that x^3 + y^3 = (x+y)(x^2 - xy + y^2)

Now, we know x + y and x^2 + y^2.

(x+y)^2 = x^2 + 2xy + y^2 (expansion)

(10)^2 = 60 + 2xy

20 = xy

x^3 + y^3 = (x+y)(x^2 - xy + y^2) = (10)(60 - 20) = 400.

Note: you can also find the values of x and y, which happen to be 5+sqrt(5) and 5-sqrt(5), but cubing these values without a calculator is very tedious and it is much easier simply to manipulate the cubes into things already given or easily found (like xy).