Answer:
x = 3 only
Step-by-step explanation:
[tex]\sqrt{2x-5} =1+\sqrt{x-3}[/tex]
[tex]\implies 2x-5=(1+\sqrt{x-3})^2\\\\ \implies 2x-5=x+2\sqrt{x-3} -2[/tex]
[tex]\implies x-3=2\sqrt{x-3}[/tex]
[tex]\implies (x-3)^2=(2\sqrt{x-3})^2[/tex]
[tex]\implies x^2-6x+9=4x-12[/tex]
[tex]\implies x^2-10x+21=0[/tex]
[tex]\implies (x-3)(x-7)=0[/tex]
[tex]\implies x=3, x=7[/tex]
Check by substituting found values of x into original equation:
[tex]x=3 \implies \sqrt{2(3)-5} =1+\sqrt{3-3} \implies 1 = 1 \ \ \ \checkmark[/tex]
[tex]x=7 \implies \sqrt{2(7)-5} =1+\sqrt{7-3} \implies 3\neq 2 \ \ \ \ incorrect[/tex]
