SOLUTION: 1.) Solve: sqrt x-3 = sqrt 2 - sqrt x for x 2.) Solve: sqrt 2y-6 = 3-y for y 3.) Solve: 5 - sqrt 20x + 4 greater than equal to -3 4.) The solution to sqrt 3x + 4 greater

Algebra.Com
Question 996546: 1.) Solve: sqrt x-3 = sqrt 2 - sqrt x for x
2.) Solve: sqrt 2y-6 = 3-y for y
3.) Solve: 5 - sqrt 20x + 4 greater than equal to -3
4.) The solution to sqrt 3x + 4 greater than equal to 2 is x greater than or equal to 0 (true or false)

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Solve: sqrt x-3 = sqrt 2 - sqrt x for x
-----------------------------------------

= - .

Square both sides. You will get

= - + .

Simplify:

- = -

= .

Square both sides again:

25 = 8x.

x = .

Check:  Left side is    = = = = .

            Right side is    - = - = - = = .

The results for the left side and the right side are different.

It means that the original equation has no solutions.  (The solution that we obtained is the solution to the equation
with the squared left and right sides of the original equation,  but it doesn't satisfy the original equation.
Again,  it means that the original equation has no solutions).

The plots in the Figure below confirm this conclusion.




Plots:  (red);    (green);    (blue).


RELATED QUESTIONS

1.) The solution to sqrt 2x+3 - sqrt x-1=1 is x=3? true or false 2.) The solution to... (answered by ikleyn)
Solve the equation... (answered by Alan3354)
sqrt(x+3)+1=sqrt(3x-2) Solve for... (answered by mananth)
a) 6+ sqrt( x-y) = x+y+ 3sqrt(2) b) xy+ sqrt( x+y) = 5/4 + sqrt(3) c) x+y sqrt(5) =... (answered by ikleyn)
(sqrt(x-2)) + 4 - (sqrt(x+2)) + (sqrt(3)) =... (answered by jsmallt9)
Solve the following equations. a) sqrt x - 1 = 3 b) sqrt (x^3) = 8 c) ^3 sqrt... (answered by uma)
Solve the equation. sqrt 2x + 5 - sqrt x - 2 =... (answered by Alan3354)
Solve the equation sqrt (2x + 5) - sqrt (x - 2) =... (answered by monika_p,Mathtut)
Please help me regarding this question. Solve for x and y by subsitution method. (answered by mananth)