ABCD

Algebra Level 3

$a , b , c , d > 0$

$a + b + c + d = 12$

$abcd = 27 + ab + ac + ad + bc + bd + cd$

1 solution

Deepanshu Gupta
Dec 14, 2014

By Simple using AM-GM inequality , we get

${ (abcd) }_{ max }\quad =\quad 81\\ \\ { (\sum { ab } ) }_{ min }\quad =\quad 54$ . But acc. to given Constrained in question ,

$\\ \sum { ab } \quad +\quad 27\quad =\quad abcd$ .

Equality of Variables must be attained

$a\quad =\quad b\quad =\quad c\quad =\quad d\quad =\quad 3$ .

Ans = 24 , Q.E.D

Now This question is correct Please Kindly Review it and Remove Flag from this ! @Calvin Lin Sir

Deepanshu Gupta - 6 years, 6 months ago

Thanks. I see that this problem has been rephrased, and 24 is now correct.

Those who previously answered 72 have been marked correct.

Calvin Lin Staff - 6 years, 6 months ago