\(x+y=4\\ \Rightarrow\left(x+y\right)^2=16\\ \Rightarrow x^2+y^2+2xy=16\\ \Rightarrow2xy=6\\ \Rightarrow xy=3\\ \left(x+y\right)\left(x^2+y^2\right)=40\\ \Rightarrow x^3+y^3+xy\left(x+y\right)=40\\ \Rightarrow x^3+y^3+3.4=40\\ \Rightarrow x^3+y^3=28\\ \)
Ta có : xy=3
=> x^2.y^2=9
\(x^6+y^6\\ =\left(x^3\right)^2+\left(y^3\right)^2\\ =\left(x^3+y^3\right)^2-2x^3y^3\\ =28^2-2.9\\ =784-8=766\)
Ta có: \(x+y=4\Leftrightarrow x^2+2xy+y^2=4\)
\(\Leftrightarrow2xy=-6\)
\(\Leftrightarrow xy=-3\)
\(\Leftrightarrow x^2y^2=9\)
Lại có: \(x^2+y^2=10\)
\(\Leftrightarrow x^6+3x^4y^2+3x^2y^4+y^6=1000\)
\(\Leftrightarrow x^6+y^6+3x^2y^2\left(x^2+y^2\right)=1000\)
\(\Leftrightarrow x^6+y^6=730\)
Vậy...
\(x+y=4\Leftrightarrow x^2+y^2+2xy=16\)
\(\Leftrightarrow xy=3\Leftrightarrow x^2y^2=9\)
Ta có: \(x^2+y^2=10\)
\(\Leftrightarrow x^6+y^6+3x^2y^2\left(x^2+y^2\right)=1000\)
\(\Leftrightarrow x^6+y^6=730\)
x2 + y2 = 10
=> ( x + y)2 - 2xy = 10
=> 16 - 2xy = 10
=> -2xy = -6
=> xy = 3
Ta có :
x6 + y6
= ( x2)3 + ( y2)3
= ( x2 + y2)( x4 - x2y2 + y4)
= 10[ ( x2 + y2)2 - 2x2y2 - x2y2]
= 10( 100 - 27 )
= 10.73
= 730
