Question

Cho \(x^3-y^3=335,x-y=5\). Tính xy.

Answer 1

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

=>\(5^3+3\cdot xy\cdot5=335\)

=>\(15xy=335-125=210\)

=>xy=14

x-y=5

=>x=y+5

xy=14

=>\(y\left(y+5\right)=14\)

=>\(y^2+5y-14=0\)

=>(y+7)(y-2)=0

=>\(\left[{}\begin{matrix}y=-7\\y=2\end{matrix}\right.\)

Khi y=-7 thì x=y+5=-7+5=-2

Khi y=2 thì x=y+5=2+5=7