#rarrsqrt(x-1)+sqrt(2x)=3#
#rarrsqrt(x-1)=3-sqrt(2x)#
#rarr[sqrt(x-1)]^2=[3-sqrt(2x)]^2#
#rarrx-1=9-6sqrt(2x)+2x#
#rarr6sqrt(2x)=x+10#
#rarr[6sqrt(2x)]^2=[x+10]^2#
#rarr36*(2x)=x^2+20x+100#
#rarrx^2-52x+100=0#
#rarrx^2-2*x*26+26^2-26^2+100=0#
#rarr(x-26)^2=26^2-100=576#
#rarrx-26=sqrt(576)=+-24#
#rarrx=26+24,26-24=50 or 2#
Putting #x=50# in given equation, we get,
#rarrsqrt(50-1)+sqrt(2*50)=17(rejected)#
Putting #x=2# in given equation, we get,
#rarrsqrt(2-1)+sqrt(2*2)=3(accepted)#
So, the required value of x is #2.#