Solve. Look at equation. Ty!

Question

anonymous · Answer

$$\sqrt{x-1}+\sqrt{4x-3}=1$$
I notice that if I square both sides it won't work out...

tkhunny · Answer

You must do two things before you do that.

1) Think abvout the Domain.  That way, if anything goes wrong, you will see it.
2) Isolate one fo the radicals and THEN square both sides.

1a) $x - 1 \ge 0$  Why?
1b) $4x-3 \ge 0$  Why?

anonymous · Answer

Yes i'm advanced in theory so i understand the domain but i still don't know how to solve isolating one radical

anonymous · Answer

$$\sqrt{x-1}=1-\sqrt{4x-3}$$
$$(\sqrt{x-1})^2=(1-\sqrt{4x-3})^2$$
$$x-1=1-2\sqrt{4x-3}+(4x-3)$$
$$2\sqrt{4x-3}-3x=-1$$

anonymous · Answer

With
$$4x-3\ge0$$
$$x \ge \frac{ 3 }{ 4 }$$ then...(?)

hartnn · Answer

with 
$2\sqrt{4x-3}-3x=-1$
again isolate $2\sqrt{4x-3}$
and square both sides to remove the remaining square root sign.

anonymous · Answer

Thank you hartnn I'm not sure why  I stopped where I stopped, thank you so much for answering!!!

hartnn · Answer

hey, welcome ^_^