Given:
[tex]x-5=\sqrt{x-3}[/tex]
To find:
The solution
Explanation:
Taking square on both sides, we get
[tex](x-5)^2=x-3[/tex]
Expanding and solving for x, we get,
[tex]\begin{gathered} x^2+25-10x=x-3 \\ x^2+25-10x-x+3=0 \\ x^2-11x+28=0 \\ (x-7)(x-4)=0 \\ x=7,4 \end{gathered}[/tex]
Therefore, the solutions are 7 and 4.
Final answer:
The solutions are 7 and 4.
