Question

Cho \(x-y=5\) và \(x^2+y^2=15\) Tính \(x^3-y^3\)

Answer 1

Có: \(\left(x-y\right)^2=25\)

\(\Leftrightarrow-2xy=25-\left(x^2+y^2\right)=25-15=10\)

\(\Leftrightarrow xy=-5\)

\(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)=5\cdot\left(15-5\right)=5\cdot10=50\)

Answer 2

   x - y = 5

=>(x - y)^{2 ​}= 25

​=> x²  - 2xy + y^{2 ​} = 25

​=> 15 - 2xy ^​ =​ 25

=>  2xy = 15 - 25

=> 2xy = - 10

=> xy = -10 : 2

=> xy = -5

x^{3 ​} - y^3​  =​ ( x - y ) ( x ²  - xy + y²)​​

^​​​ => x³- y^{3 ​}= 5 . ( -5 . 15 )

​= >x ^{3  ​} -​ y ^3​ = - 375. ​

Answer 3

Violympic ak?????