if (a,1/a),(b,1/b)&(c,1/c)are the vertices of a triangle,(a,b) are roots of x2-6p1x+2=0,(b,c)roots of x2-6p2x+3=0&(c,a)roots of x2-6p3x+6=0.p1,p2,p3being positive,find p1,p2,p3¢roid of triangle.

Dear jagannath

(a,b) are roots of x2-6p1x+2=0

a+b=6p_{1  ............1}

ab=2 .............2

(b,c)roots of x2-6p2x+3=0

b+c=6p_{2............3}

bc=3..........4

(c,a)roots of x2-6p3x+6=0

c+a=6p_{3 .............5}

ca=6 .............6

from equation 2,4,6

(ab)(bc)=ca

b=1

and a=2

c=3

so P1 =1/2

p2 =2/3

P3=5/6

now centroid ={(1+2+3)/3    ,(1/2 +1/1  +1/3 )/3 }

                          (2,11/18)