Question

x-y=5
x^2+y^2=15

x^3-y^3=?

Answer 1

`x-y=5`

`<=>(x-y)^2=25`

`<=>x^2-2xy+y^2=25`

`<=>15-2xy=25`

`<=>2xy=-10`

`<=>xy=-5`

`=>x^3-y^3`

`=(x-y)(x^2+xy+y^2)`

`=5.(15-5)`

`=5.10=50`

Answer 2

Ta có: \(x-y=5\)

\(\Leftrightarrow x^2+y^2-10xy=25\)

\(\Leftrightarrow15-10xy=25\)

\(\Leftrightarrow10xy=-10\)

hay xy=-1

Ta có: \(x^3-y^3\)

\(=\left(x-y\right)^3+3xy\left(x-y\right)\)

\(=5^3+3\cdot5\cdot\left(-1\right)\)

\(=125-15=110\)