SOLUTION: 1.) (6b)^1/2 = (8-2b)^1/2
2.) (18-n)^1/2 = (n/8)^1/2
3.) (-3-4x)^1/2 - (-2-2x)^1/2 = 1
4.) x = 5+(3x-11)^1/2
Algebra.Com
Question 841811: 1.) (6b)^1/2 = (8-2b)^1/2
2.) (18-n)^1/2 = (n/8)^1/2
3.) (-3-4x)^1/2 - (-2-2x)^1/2 = 1
4.) x = 5+(3x-11)^1/2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.) (6b)^1/2 = (8-2b)^1/2
Square both sides to get:
6b = 8-2b
8b = 8
b = 1
-----------------------------------------
2.) (18-n)^1/2 = (n/8)^1/2
Square both sides to get:
18-n = n/8
(9/8)n = 18
n = 2*8 = 16
-----
Note n = 16 would make the left side
of your problem imaginary.
---
Conclusion: No solution
---------------------------------------------
3.) (-3-4x)^1/2 - (-2-2x)^1/2 = 1
Square both sides:
-3-4x + -2-2x - 2((-3-4x)(-2-2x)))^(1/2) = 1
---------
Rearrange and square both sides to get:
=========
(-5-6x-1)^2 = [2(6+14x+8x^2)]
(-6-6x)^2 = 12 + 28x+16x^2
36+72x+36x^2 = 12 + 28x + 16x^2
20x^2 + 44x + 24 = 0
5x^2 + 11x + 6 = 0
Factor:
5x^2+5x + 6x + 6 = 0
5x(x+1) + 6(x+1) = 0
(x+1)(5x+6) = 0
x = -1 or x = -6/5
--------------------
Note: Check for extraneous solutions.
--------------------
4.) x = 5+(3x-11)^1/2
(3x-11)^(1/2) = x-5
Square both sides to get::
3x-11 = x^2-10x+25
x^2 - 13x + 36 = 0
x^2 - 9x-4x + 36 = 0
x(x-9)-4(x-9) = 0
(x-9)(x-4) = 0
x = 9 or x = 4
-----
Cheers,
Stan H.
----------------
RELATED QUESTIONS
(6b)^1/2 =... (answered by ewatrrr)
{{{ (8*n^2-1)(3*n^2-4*n+5)... (answered by kingme18)
(18-n)^1/2 =... (answered by ewatrrr)
(n+1/3)+(n+2/4)=1 (answered by jim_thompson5910)
1/4x-3/8(3x-1/2)=-x-1/8 (answered by faceoff57)
-2(n+1)-3<1 (answered by cathieb1225)
(n+1)!={11*(n-1)/2}*{(n+3)!/3!},solveforn (answered by greenestamps)
6b-2b+1=5b+2-2 (answered by tommyt3rd)
(2^n-3)*(8^n+1)/(2^2n-1)*(4^2-n) (answered by jsmallt9)