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Solve equation sq root(1+3x)=x-1?

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yapayapa | Honors

Posted July 14, 2013 at 5:32 PM via web

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Solve equation sq root(1+3x)=x-1?

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 14, 2013 at 7:14 PM (Answer #2)

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Solve `sqrt(1+3x)=x-1` :

`sqrt(1+3x)=x-1`  Square both sides:

** Be aware that squaring can create extraneous solutions -- solutions that follow algebraically but do not work in the original equation **

`(sqrt(1+3x))^2=(x-1)^2`

`1+3x=x^2-2x+1`

`x^2-5x=0`

`x(x-5)=0`

x=0 or x=5

Check for extraneous solutions:

If x=0 then `sqrt(1+3(0))=(0)-1 ==> 1=-1` which is not true so x=0 is extraneous.

If x=5 then `sqrt(1+3(5))=(5)-1 ==> 4=4`

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The solution is x=5

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The graphs of the left side and right side -- the solution(s) is/are the points of intersection:

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 14, 2013 at 7:15 PM (Reply #1)

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This is incorrect. x=0 is extraneous. You have found the intersections of the line y=x-1 and the parabola `x=1/3(y^2-1)` ; however we are given the function representing the upper half of the parabola only.

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