the minimum value of 3^{(x.x -2)(x.x -2)(x.x -2)(x.x -2)(x.x -2) +32}

is

Dear Sonny,

The expression is minimum when the power is minimum.
since the terms are positive the least possible value is 0.
this can only be attained if all (x.x -2)=-2,
then only 32-32=0
Hence x.x=0=>x=0
minimum value= 3^0
= 1 (ANS).

Regards

we know that any positive integer to the power any real number is positive.so the expression cannot have negative value.so least value is 0.

now, for the expression to be minimum,its power has to be minimum that is 0.

so x(x-2)=2

or x*x-2x-2=0,which is possible.

hence the minimum value is 3 to the power 0,that is 1.

The expression is minimum when the power is minimum.
since the terms are positive the least possible value is 0.
this can only be attained if all (x.x -2)=-2,
then only 32-32=0
Hence x.x=0=>x=0
minimum value= 3^0
= 1 (ANS).

Regards