Terms want Freedom

Algebra Level 5

Given $p$ and $q$ are positive real numbers that satisfy the equation $p^4 + q^3 = 2$ . What is the maximum value of the term independent of $x$ in the expansion below?

$\large \left ( p \space x^{\frac {1}{12}} + q \space x^{-\frac {1}{9}} \right )^{14}$

Practice the set Target JEE_Advanced - 2015 and boost up your preparation.

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The answer is 3003.000.

1 solution

Deepanshu Gupta
Mar 4, 2015

too easy ! , here P=1 , q=1 , (AM=GM) and answer is C(14,6) . Hint : Find 7th term of Binomial expansion.

Seriously overrated!!!

Adarsh Kumar - 6 years, 3 months ago

I too think, it's overrated. Okay, I'm taking it to the level 4, then it will be fine.

Sandeep Bhardwaj - 6 years, 3 months ago

Thank you sir!But isn't Level 4 and that too 160 points is a bit too high.It is a simple application of Binom and AM-GM.110 points should be enough!Just a suggestion.

Adarsh Kumar - 6 years, 3 months ago

@Adarsh Kumar – I think points get adjusted automatically depending on the number of incorrect answers. So, let it go its way :P

Sandeep Bhardwaj - 6 years, 3 months ago

@Sandeep Bhardwaj Sir why you unnessecerily make answer as decimal ? I don't think there is need to confuse everyone !

Karan Shekhawat - 6 years, 3 months ago

hehehe... It checks How sure you're about your ans !!! @KARAN SHEKHAWAT

Sandeep Bhardwaj - 6 years, 3 months ago

@Sandeep Bhardwaj !! seriously .. i checked like three times before typing.. not fair!! :P

Ramesh Goenka - 6 years, 3 months ago

Terms want Freedom

Practice the set Target JEE_Advanced - 2015 and boost up your preparation.

Image Credit: Wikimedia Pascal-animation

The answer is 3003.000.

1 solution

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