Question

sqrt{3x-5}=2-sqrt{x-1}

Answer 1

Square both sides.

Answer 2

\[3x-5=4-4\sqrt{x-1}+x-1\]

Answer 3

find all real and imaginary solutions to equation

Answer 4

\[2x-8=4\sqrt{x-1}\]

Answer 5

Now divide both sides by 2 and then square both sides again.

Answer 6

\[x-4=2\sqrt{x-1}\]

Answer 7

\[2x-8=-4\sqrt{x-1}\]

Answer 8

\[x^2-8x+16=4(x-1)\]

Answer 9

mertsj did you see kropots answer it would be -4

Answer 10

@kropot72 The negative makes no difference. You're about to square it anyway.

Answer 11

gotcha ty

Answer 12

If it makes you feel better, we can include it?
\[x-4=-2\sqrt{x-1}\]

Answer 13

Now square both sides.

Answer 14

no i see your point

Answer 15

\[x ^{2}=12x-20\]

Answer 16

Collect all the terms onto the left hand side and you will have a quadratic to solve

Answer 17

x-10 and x-2 are my answers

Answer 18

x = 10 and x = 2 are the solution

Answer 19

ty kropot72 and mertsj

Answer 20

All credit to mertsj.