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Q.

Tangent at the point P(1,1) on the curve y=x2+bxb meets the positive x and y axes at A and B respectively and O is the origin. If b1,b2,b3 are the values of b for which the area of triangle OAB is 2 sq. units with b1<b2<b3 then |b1|+|b2+b3|=_______

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answer is 5.

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Detailed Solution

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m=dydx(1,1)=b+2
Tangent is y1=(b+2)(x1)
(b+2)xy(b+1)=0 
Area of ΔOAB is 2
(b+1)22(b+2)=2b2+2b+1=±4(b+2)
b2+6b+9=0 (or) b22b7=0
b1=3   ,    b2+  b3=2
|b1|+|b2+b3|=5

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