Latest TCS Aptitude Question SOLUTION: what is the max value of x3y3+3xy,when x+y=8? A.4144 B.256 C.8192 D.102

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what is the max value of x3y3+3xy,when x+y=8?
A.4144
B.256
C.8192
D.102

Asked In TCS venkata swamy (10 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

RAKESH  (10 years ago)

f(x)= x^3*y^3+3xy is a homogeneous function , maxm value of f(x)occurs at x=y

x+y=8 & x=y => x=y=4
put the value (x,y)=(4,4) in f(x) to get max value of f(x)

f(x)max = 4^3*4^3 + 3*4*4 = 4144

Is this solution Helpfull? Yes (21) | No (3)  

R.RAVIKUMAR  (10 years ago)

Ans:4144

To know the (x,y) which gives max we have to derivate the given eqn..
by derivating that we get 3x^2y^2(x+y)+3(x+y)
by using x+y=8, 24(x^2y^2+1) ----- (1)

the possible combinations for x+y=8 are
(0,8),(1,7),(2,6),(3,5),(4,4),(5,3),(6,2),(7,1),(8,0)
we get max value at (4,4) for eqn (1)..
so now the (x,y)=(4,4)

substituting them original eqn,
((4^3)(4^3))+3(4*4)=4144

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karthi  (10 years ago)

the max value wen x+y=8(take x=4 y=4)..
then [(4^3)*(4^3)*]+(3*4*4)=(4096+48)=4144

Is this solution Helpfull? Yes (4) | No   

sabitha.p  (10 years ago)

x+y=8
consider possibles of 8(4+4)(6+2)(5+3)(1+7)
from this apply the values in x3y3+3xy
so the answer is 4144

Is this solution Helpfull? Yes (1) | No (3)  

UTKALA PADMA PRIYA SRUNGARAM  (10 years ago)

given x+y=8, let us take x=4 and y=4
substitute this in the given equation we get 4144

Is this solution Helpfull? Yes (1) | No (2)  

Vincy S  (10 years ago)

A.4144
the possibilities of x and y vales are(1,7)(2,6)(3,5)(4,4)
Take X=4 and Y=4 by sub these values in given equ.it gives only the max values

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RITESH KUMAR  (9 years ago)

x+y=8 will gives xy max when x=y so x=y=4
now x^3*y^3+3xy=(xy)^3+3xy=16^3+16*3=4096+48=4144

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