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jagannath singh Grade:
        

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.

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear jagannath


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


a+b=6p1  ............1


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


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


b+c=6p2............3


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


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


c+a=6p3 .............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)





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7 years ago
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