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Question

If the line y=22x cuts the curve x3+y3+6xy+6x2+2y2+5x+5y+1=0 at the point A,B,C then OA.OB.OC is equal to a(116b)c. Find a+b+c.

(where O is the origin)

A
511
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B
540
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C
420
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D
340
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Solution

The correct option is B 540

Given Equation of curve:

x3+y3+6xy+6x2+2y2+5x+5y+1=0

Substituting y=22x in the above curve

(162+1)x3+(22+122)x2+(5+102)x+1=0

Product of roots =da=1162+1=1162511

OA=x21+(22x1)2=9x21=3x1

OA.OB.OC=27x1x2x3

=27(1162)511=a(116b)c

So,

a+b+c=27+2+511=540


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