Helpp. . . .Solve each equation. Check for extraneous solutions. . .

Question

anonymous · Answer

$$-3=\sqrt{4-n}-\sqrt{6n-2}$$

anonymous · Answer

To solve this equation we need to first get one of the square roots on the other side or the equation, in this case lets add root 6n-2 to booth sides of the equation....

anonymous · Answer

now lets square both sides

anonymous · Answer

after squaring the equation looks like this: 7-6root6n-2+6n=4-n

anonymous · Answer

I don't understand that
why is there still a square root?

anonymous · Answer

well we are not done yet, but to answer your question....

anonymous · Answer

shouldn't it be 9+6n-2=4-n?

anonymous · Answer

-3+root 6n-2=root 4-n, we square both sides, this gives us: 9-3root 6n-2-3root 6n-2+6n-2 on the left hand side and of course squaring  roo 4-n just give us 4-n  on the right side

anonymous · Answer

What? Can you use the equation writer please?

anonymous · Answer

$$(-3+\sqrt{6n-2})^2=\sqrt{4-n}^2$$

anonymous · Answer

OH! Nevermind, I understand now.

anonymous · Answer

Hahaa, sorry

anonymous · Answer

Okay continue.