Cho `x+y =2` `x.y=-1` Tính `a x^2 +y^2` `b) x^3 + y^3` `c) x^4 +y^4` `d) x^5 + y^5` `e) x^6 + y^6`

1 bình luận về “Cho `x+y =2` `x.y=-1` Tính `a x^2 +y^2` `b) x^3 + y^3` `c) x^4 +y^4` `d) x^5 + y^5` `e) x^6 + y^6`”

1. a)x^2+y^2

   =x^2+2xy+y^2-2xy

   =(x+y)^2-2.(-1)

   =2^2+2

   =4+2

   =6

   b)x^3+y^3

   =x^3+3x^2 y+3xy^2+y^3-3x^2 y-3xy^2

   =(x+y)^3-3xy(x+y)

   =2^3-3.(-1).2

   =8+6

   =14

   c)x^4+y^4

   =(x^2)^2+2x^2 y^2+(y^2)^2-2x^2 y^2

   =(x^2+y^2)^2-2.(xy)^2

   =6^2-2.(-1)^2

   =36-2.1

   =36-2

   =34

   d)(x^2+y^2)(x^3+y^3)=6.14

   =>x^5+x^2 y^3+x^3 y^2+y^5=84

   =>x^5+x^2 y^2 .(x+y)+y^5=84

   =>x^5+(xy)^2 .2+y^5=84

   =>x^5+(-1)^2 .2+y^5=84

   =>x^5+y^5+2=84

   =>x^5+y^5=82

   e)(x^2+y^2)(x^4+y^4)=6.34

   =>x^6+x^2 y^4+x^4 y^2+y^6=204

   =>x^6+x^2 y^2 (x^2+y^2)+y^6=204

   =>x^6+(xy)^2 .6+y^6=204

   =>x^6+(-1)^2 .6+y^6=204

   =>x^6+y^6+6=204

   =>x^6+y^6=198

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