Show that the function #g(x)=sqrt(x-5)-1/(x+3)# has at least a real root?

1 Answer
Apr 11, 2018

#color(blue)(x=5)#

Explanation:

#sqrt(x-5)-1/(x+3)=0#

Add #1/(x+3)#

#sqrt(x-5)=1/(x+3)#

Squaring:

#x-5=1/(x+3)^2#

Multiply by #(x+3)^2#

#(x+3)^2(x-5)=1#

#(x+3)^2(x-5)-1=0#

Factor:

#(x-5)[(x+3)^2-1/(x-5)]=0#

#x-5=0=>color(blue)(x=5)#