SOLUTION: 1.) (6b)^1/2 = (8-2b)^1/2 2.) (18-n)^1/2 = (n/8)^1/2 3.) (-3-4x)^1/2

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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
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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
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Note n = 16 would make the left side
of your problem imaginary.
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Conclusion: No solution
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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
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Rearrange and square both sides to get:
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(-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
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Note: Check for extraneous solutions.
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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
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Cheers,
Stan H.
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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