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# u substition

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OK, I'm going through my lab final - I'm having a difficult time with ALL OF IT...LOL  Yes, I'm not good at higher math.  And this is probably basic algebra....

My question is x-2x^1/2-3= 0  and use u substitution. My answer is x=9

Guest May 13, 2017
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x- 2x^(1/2) - 3= 0

Let x = u^2  ...so.....x^(1/2)  =  u   and we have

u^2  - 2u - 3  = 0           factor

(u - 3)  ( u + 1)  = 0      set both factors  equal to 0 and solve

u - 3  = 0                                u +  1    = 0

add 3 to both sides            subtract 1 from both sides

u  = 3                                 u  = -1

So

u^2  = 3^2  = 9  = x       or       u^2 = (-1)^2  =  1  = x

The second solution makes the original problem false......so...... x = 9  is the only solution

CPhill  May 13, 2017
edited by CPhill  May 13, 2017

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