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The graphs of y = 3 - x + x^3 and y = 1 + x + x^2 + x^3 The graphs of  and  intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.

 Feb 22, 2021
 #1
avatar+804 
0

1 + x + x^2 + x^3 = 3 - x + x^3

1 + x + x^2 = 3 - x

x^2 + 2x - 2 = 0

 

So, we can use the quadratic equation to find the 2 ys, or we can simpify it a bit first. 

(-b+sqrt(b^2-4ac))/2a- (-b-sqrt(b^2-4ac))/2a = sqrt(b^2-4ac)/a

Now, the difference is sqrt(b^2 - 4ac). 

 

 

sqrt(2^2 - 4(-2))/1

sqrt(8)

2sqrt(2)

 

I hope this helped. :))

 

=^._.^=

 Feb 22, 2021
 #3
avatar+804 
0

Looking at ElectricPavlov's graph, my answer is not right. 

 

=^._.^=

catmg  Feb 22, 2021
 #2
avatar+30677 
+1

Equate the two polynomials and solve for the x points of intersection

 

3-x = 1+x+x^2

x^2 +2x -2 = 0

 

 

Well it said 'graphing' in the Q ....so here is the graph of the two polynomials

 

  I think you can take it from here !

 

 Feb 22, 2021

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