The number of real solutions of the equation [9/x]^x=-3+x-x^2 is?

1 Answer
Sonnhard
Jul 16, 2018

No real Solutions.

Explanation:

For #x>0# is #(9/x)^x>0# (for #x<0# is #(9/x)^x# not defined, #x# as a real number)

and for #x>0# is

#-3+x-x^2<0#
multiplying by #-1#

#x^2-x+3>0#
and this is

#x^2-2*(1/2)*x+1/4+3-1/4>0#

#(x-1/2)^2+11/4>0# which is true for all #x# with #x>0#

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