\(x^4+y^4\)
\(=x^4+2x^2y^2-2x^2y^2+y^4\)
\(=\left(x^4+2x^2y^2+y^4\right)-2.x.x.y.y\)
\(=\left(x^2+y^2\right)^2-2.x.y.x.y\)
\(=\left(x^2+2xy-2xy+y^2\right)^2-2.x.y.x.y\)
\(=\left[\left(x^2+2xy+y^2\right)-2xy\right]^2-2.x.y.x.y\)
\(=\left[\left(x+y\right)^2-2xy\right]^2-2.x.y.x.y\)
Thay x+y=-3 và x.y=12 vào biểu thức ta có:
=>\(\left[\left(-3\right)^2-2.12\right]^2-2.12.12\)
\(=\left(9-24\right)^2-288\)
\(=255-288\)
\(=33\)
\(x^2+y^2=\left(x+y\right)^2-2xy=9-24=-15\)
=>Đề sai rồi bạn
x4+y4x4+y4
=x4+2x2y2−2x2y2+y4=x4+2x2y2−2x2y2+y4
=(x4+2x2y2+y4)−2.x.x.y.y=(x4+2x2y2+y4)−2.x.x.y.y
=(x2+y2)2−2.x.y.x.y=(x2+y2)2−2.x.y.x.y
=(x2+2xy−2xy+y2)2−2.x.y.x.y=(x2+2xy−2xy+y2)2−2.x.y.x.y
=[(x2+2xy+y2)−2xy]2−2.x.y.x.y=[(x2+2xy+y2)−2xy]2−2.x.y.x.y
=[(x+y)2−2xy]2−2.x.y.x.y=[(x+y)2−2xy]2−2.x.y.x.y
Thay x+y=-3 và x.y=12 vào biểu thức ta có:
=>[(−3)2−2.12]2−2.12.12[(−3)2−2.12]2−2.12.12
=(9−24)2−288=(9−24)2−288
=255−288=255−288
=33
