Question

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

x^3-y^3=?

 

Answer 1

\(\left\{{}\begin{matrix}x-y=5\\x^2-y^2=15\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x-y=5\\x+y=3\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-1\end{matrix}\right.\)

\(x^3-y^3=4^3-\left(-1\right)^3=65\)

Answer 2

x²-y²=15 

⇒(x-y)(x+y)=15

⇒ 5(x+y)=15

⇒ x+y=3

x-y=5, x+y=3⇒x-y+x+y=5+3

                    ⇒ 2x=8 

                    ⇒ x=4

x+y=3 ⇒ 4+y=3

          ⇒ y=-1

x³-y³=4³-(-1)³=64+1=65

Answer 3

Có : `x^2-y^2=15`

`->(x-y)(x+y)=15`

`->5(x+y)=15`

`->x+y=3`

Mà `x-y=5`

`->x=4;y=-1`

`->x^3+y^3=4^3-(-1)^3=64+1=65`

Answer 4

Ta có: \(\left\{{}\begin{matrix}x-y=5\\\left(x-y\right)\left(x+y\right)=15\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y=5\\x+y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=8\\x+y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-1\end{matrix}\right.\)

Ta có: \(x^3-y^3\)

\(=4^3-\left(-1\right)^3\)

=64+1

=65