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If $x^2 + y = 4$ and $x^4 +y^2 = 10$, then what is $x^2y$?

 Jun 20, 2019

Best Answer 

 #1
avatar+8962 
+3

x2 + y   =   4

                            Square both sides of the equation.

(x2 + y)2  =  42

                                       Expand the left side.

(x2 + y)(x2 + y)  =  16

 

x4 + 2x2y + y2  =  16

                                       Rearrange the terms on the left side.

2x2y + x4 + y2  =  16

                                       Since  x4 + y2 = 10  we can substitute  10  in for  x4 + y2

2x2y + 10  =  16

                            Subtract  10  from both sides.

2x2y  =  6

                            Divide both sides by  2

x2y  =  3

 Jun 20, 2019
 #1
avatar+8962 
+3
Best Answer

x2 + y   =   4

                            Square both sides of the equation.

(x2 + y)2  =  42

                                       Expand the left side.

(x2 + y)(x2 + y)  =  16

 

x4 + 2x2y + y2  =  16

                                       Rearrange the terms on the left side.

2x2y + x4 + y2  =  16

                                       Since  x4 + y2 = 10  we can substitute  10  in for  x4 + y2

2x2y + 10  =  16

                            Subtract  10  from both sides.

2x2y  =  6

                            Divide both sides by  2

x2y  =  3

hectictar Jun 20, 2019

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