Question

Help me please

Answer 1

the least value of the product xyz for which the determinant ( the diagonalic elements are x, y, z respectively the other elements are 1) is non-negative
A)-2sqrt2
B)-8
C)-16sqrt2
D)-1

Answer 2

@Michele_Laino may u please help me :)
ill brb

Answer 3

hint:
we have to minimize this function:
\[\Large f\left( {x,y,z} \right) = xyz - x - y - z\]

Answer 4

well
i am not getting what to do

Answer 5

@Michele_Laino please help :)

Answer 6

is there any more information given in the problem

Answer 7

no

Answer 8

ok the determinant is
x*y*z-x-y-z+2

Answer 9

yes

Answer 10

yeah

Answer 11

please explain :)

Answer 12

Shoudln't we find a relation between z,y,x ?

Answer 13

i think the answer is -1

Answer 14

@perl

Answer 15

help please

Answer 16

@behappy
you're supposed to do this is a Lagrange multiplier, right?

if not, pls ignore this post.

if so, you have to minimise xyz, as the question requests, whilst still having x*y*z-x-y-z+2 as non negative, ie your condition is x*y*z-x-y-z+2 >0

so, in familiar notation, you have:
f(x,y,z) = xyz
g(x,y,z) = x*y*z-x-y-z+2

so solve:
\[\nabla f = \lambda \nabla g\]
and
\[g(x,y,z) = xyz-x-y-z+2 > 0\]

it should look like this, when done:
https://www.wolframalpha.com/input/?i=solve+x%5E3+-+3x+%2B+2+%3D+0