Question 245958: g(x) = √( x - 1) + √(2x), find all values of x for which g(x) = 6
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! g(x) = √( x - 1) + √(2x), find all values of x for which g(x) = 6
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Substitute to get:
sqrt(x-1) + sqrt(2x) = 6
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Square both sides to get:
(x-1) + 2(sqrt(2x(x-1)) + 2x = 36
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2sqrt(2x^2-2x) + 3x -1 = 36
2sqrt(2x^2-2x) = -(3x-37)
Square both sides to get:
4[2x^2-2x] = 9x^2-222x+1369
8x^2-8x = 9x^2-222x+1369
x^2 - 214x + 1369 = 0
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I graphed the equation to find the solutions to get:
x = 6.601 or x = 207.40
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x=207.4 is an extraneous solution.
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Solution:
x = 6.601
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Cheers,
Stan H.
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