Suppose xy=1. Find the value of x4xy3x3y3x2y+3xy2+y4.


Answer:

1

Step by Step Explanation:
  1. Given xy=1
    We need to find the value of x4xy3x3y3x2y+3xy2+y4.
  2. x4xy3x3y3x2y+3xy2+y4=(x4x3y)(xy3y4)(3x2y3xy2)[Rewriting the expression]=x3(xy)y3(xy)3xy(xy)=(xy)[x3y33xy]=(xy)[(xy)(x2+xy+y2)3xy][Using a3b3=(ab)(a2+ab+b2)]=(x2+xy+y2)3xy[Given xy=1]=x22xy+y2=(xy)2[Using (ab)2=a22ab+b2]=1[Given xy=1]
  3. Hence, the value of the given expression is 1.

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