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Q.

The maximum value of P=2a2+12b2+1+3c2+1 is _____ where a, b, c > 0 and abc+a+c= b

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An Intiative by Sri Chaitanya

a

83

b

103

c

3

d

4

answer is D.

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Detailed Solution

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a=tanA;b=tanB;c=tanC;0<A,B,C<π20<A+C<π2 P=2cos2A+3cos2C2cos2A+C

1+cos2A+32+32cos2+cos2A+2C
1+cos2A+32+32cos2Ccos2Acos2C+sin2Asin2C
32+32cos2C+1cos2Ccos2A+sin2C.sin2A
<32+32cos2C+1cos2C2+sin2C2
32+32cos2C+22cos2C=52+32cos2C+2sinC
32+3212sin2C+2sinC,  32+323sin2C+2sinC
32+323sin2C23sinC+1919=+133sec132103
 

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The maximum value of P=2a2+1−2b2+1+3c2+1 is _____ where a, b, c > 0 and abc+a+c= b