Help Solving This?

Question

1.√3-x = 2-√x+1

2.2√n + 3 = n
5
Rational Exponet Equations:

1.3x^5/2 - 9 = 0

2.(2x+3)^1/4=4

Answer 1

2. 2*sqrt(n)+3 = n.
2*sqrt(n) = n-3.
Sq. both sides:
4n = n^2 - 6n + 9
n^2-6n-4n = -9
n^2 - 10n = -9
n^2 - 10n + 9 = 0
(n-1)(n-9) = 0.
n-1 = 0, n = 1.
n-9 = 0, n = 9.
Solution set: n = 1, and 9.
If 2 terms are under radical, n=-2,and 6

Rational Exponents.
1. 3x^(5/2) - 9 = 0.
3x^(5/2) = 9
Sq. both sides:
9x^5 = 81
x^5 = 9
5*Logx = Log9
Logx = 0.190848501
X = 1.552.

2. (2x+3)^(1/4) = 4
Raise both sides to the 4th power:
(2x+3) = 256
2x = 256-3 = 253
X = 126.5.