Chapter 13 - Conic Sections - 13.2 Conic Sections: Ellipses - 13.2 Exercise Set - Page 862: 40

$x=2.5$

We have to solve $3-\sqrt{2x-1}=1$ $$3-1=\sqrt{2x-1}$$ $$2=\sqrt{2x-1}$$ Square both sides: $$4=2x-1$$ $$5=2x$$ $$x=2.5$$ Check if the solution is valid: $$3- \sqrt{2(2.5)-1}=\sqrt 4-1=2-2=1\checkmark$$ Therefore the solution is $x=2.5$.