Expert: Richard J. Raridon - 2/28/2008

Question
QUESTION: I am really struggling with these few. Is there anyway you would be able to check my work and help me with these three? √(x) + √(x + 8) = 2
√(x - 3) + √(x + 5) = 2√y
2√(x - 8) + √(x - 5) = √(x + 7)
Is there anyway you would be able to check my work for these?
√(2x-7)= -3 Answer: 8
√(8x-5) - √(7x-1) = 0 Answer: 4
x = √(x² - 2x – 4) Answer: -2
√(3x – 2) = x – 2 Answer: 1 or 6
√(-x) – 6 = x Answer: -9 or -4
³√(2x +5) = -3 Answer: -16
√(x + 4) – 1 = √(x - 1) Answer: 5

ANSWER: You can also indicate square root by ^1/2
1. x^1/2 +(x+8)^1/2 = 2, no solution
2. 2(x-8)^1/2 +(x-5)^1/2 = 2y^1/2, cannot solve one equation with two unknowns
3. 2(x-8)^1/2 +(x-5)^1/2 = (x+7)^1/2, x = 9
You could check your own work by putting the answer back in
4. (16-7)^1/2 = +/- 3
5. (32-5)^1/2 -(28-1)^1/2 = 0
6. (3x-2)^1/2 = x-2
square both sides to get 3x-2 = x^2-4x+4
so x^2 -7x +6 = 0 = (x-1)(x-6)
7. (-x)^1/2 -6 = x
(-x)^1/2 = x+6
square both sides to get -x = x^2+12x+36
x^2 +13x +36 = 0 = (x+4)(x+9)
8. (9+4)^1/2 -1 = (5-1)^1/2 or 2=2

---------- FOLLOW-UP ----------

QUESTION: Can you please show me how you got the answer? I just want to know how to work them, so next time I don't have to ask.

Greatly appreciated!

ANSWER: Which answer?

---------- FOLLOW-UP ----------

QUESTION: I need to know how to work the following:
2sqrt(x-8) +sqrt(x-5) = 2sqrt(y)
I really hate to keep bothering you and I greatly appreciate your kindness and help. Could you check to make sure I work the following correctly?
1.) sqrt(2x - 7) = -3
2x-7 = 9
2x = 16
x=8
2.) sqrt(8x-5) - sqrt(7x-1) = 0
(8x - 5) - (7x - 1) = 0
8x - 5 - 7x - 1 = 0
x - 4 = 0
x = 4
3.)x = sqry(x^2 - 2x -4)
x^2 = x^2 - 2x - 4
0 = -2x - 4
4 = -2x
x = -2
4.) sqrt(3x - 2) = x - 2
3x - 2 + x^2 - 4x + 4
0 = x^2 - 7x + 6
(x-6)(x-1)=0
x = 6 or x = 1
5.)sqrt(-x) - 6 = x
sqrt(-x) = x + 6
-x + x^2 + 13x + 36
0 = (x+9) (x+4)
x = -9 or x = -4
6.)^3sqrt(2x+5) = -3
2x + 5 = -27
2x = -32
x = -16
7.) sqrt(x+4) - 1 = sqrt(x-1)
x + 4 - 2 sqrt(x+4+1) = x-1
4 - 2 sqrt(x+4+1) = -1
sqrt(x+4) = -6
sqrt(x+4) = 3
x + 4 = 9
x = 5
8) sqrt(x) + sqrt(x+8) = 2
sqrt(x-2) = 2 + sqrt(x+8)
x-4 sqrt(x+4) = x+8
-4 sqrt(x) = 4
x = -1
THANKS AGAIN FOR YOUR KINDNESS!

Answer
For 2(x-8)^1/2 +(x-5)^1/2 = 2(y^1/2), when x=9, y=4
1) you need to realize that, when x=8, (2x-7)^1/2 gives you both
-3 and 3.
The others are okay except for (8).  I told you before that there's no solution.  x cannot = -1 since (-1)^1/2 is imaginary.