Question

x+y=2, x²+y²=10,tính A=x^3+y^3

 

Answer 1

`x+y=2`

`<=>(x+y)^2=4`

`<=>x^2+2xy+y^2=4`

`<=>10+2xy=4`

`<=>2xy=-6`

`<=>xy=-3`

`A=x^3+y^3`

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

`A=2.(10-xy)`

`A=2(10+3)=2.13=26`

Answer 2

\(x+y=2\Rightarrow\left(x+y\right)^2=4\)

\(\Leftrightarrow x^2+y^2+2xy=4\Rightarrow10+2xy=4\)

\(\Rightarrow xy=-3\)

\(A=\left(x+y\right)\left(x^2+y^2\right)-xy\left(x+y\right)=2.10-\left(-3\right).2=26\)

Answer 3

\(A=x^3+y^3\)

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

\(=2^3-3\cdot10\cdot2=8-60=-52\)