We have: #y = sqrt(x - 1) + 2#
Let's set #y# equal to zero:
#Rightarrow y = 0#
#Rightarrow sqrt(x - 1) + 2 - 0#
Subtracting #2# from both sides of the equation:
#Rightarrow sqrt(x - 1) = - 2#
Squaring both sides:
#Rightarrow (sqrt(x - 1))^(2) = (- 2)^(2)#
#Rightarrow x - 1 = 4#
Adding #1# to both sides:
#therefore x = 5#
Let's verify if this value of #x# works in the original equation:
#Rightarrow sqrt(x - 1) + 2 - 0#
#Rightarrow sqrt((5) - 1) + 2 = 0#
#Rightarrow sqrt(4) + 2 = 0#
#Rightarrow 2 + 2 = 0#
#Rightarrow 4 ne 0#
Therefore, there are no real solutions to the equation.