14 Which is the maximum value of x3y3 3 x y when x y 8 a 4144 b 256 c

In questions where sum is constant is given and then maximum value has to be found out... then we divide that constant sum in equal parts and put its value in the required equation......

x+y=8
x=8/2
y=8/2
put in equation

(4^3*4^3)+3*4*4=4144
11 years agoHelpfull: Yes(38) No(6)
a)4144.
value of expression will max when x=y.
11 years agoHelpfull: Yes(35) No(1)
we have totally 5 possibilities for x+y=8,
0,8 1,7 2,6 3,5 4,4
highest value will be given when we choose the highest number for both x and y so choose 4,4 sub in x^3*y^3+3x*y thn u will get 4144
10 years agoHelpfull: Yes(9) No(0)
X+Y=8 (MAX. CASE IS X=Y)
X=Y=4
SO. 4^3*4^3+3*4*4=4144 (ANS)
10 years agoHelpfull: Yes(6) No(1)
x=8-y
sub x in given eq: (8y-y^2)^3+3(8y-y^2)
differentiate wrt y: 3(8y-y^2)^2*(8-2y)+3(8-2y)
to find out max we equate above eq to zero:(8y-y^2)^2+3=0;8-2y=0
one eq cant be zero then other eq gives y=4
given eq is max when x=y=4
sub x=y=4 in given eq: (4*4)^3+3(4*4)=4144
ans:a
9 years agoHelpfull: Yes(3) No(0)
We have to maximize the value..So here x3y3 + 3 x*y will be maximum if x=y.So x+y=8.
x=4=y.
value=(4^3*4^3)+3*4*4=4144
8 years agoHelpfull: Yes(1) No(0)
ans is 24
11 years agoHelpfull: Yes(0) No(21)
ans is 102
6 years agoHelpfull: Yes(0) No(0)
Value of expression will be maximum when: x=y
so, x=8/2=4 and y=8/2=4.
Putting these values in given equation,
((4)^3*(4)^3)+3(4)(4) = 4144
6 years agoHelpfull: Yes(0) No(0)

14. Which is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102