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Which statement best reflects the solution(s) of the equation?

 

 Feb 9, 2018
 #1
avatar+102422 
+1

√[ 2x  - 1 ]  - x + 2  = 0    rearrange as

 

√ [2x - 1 ]  =  x  - 2         square both sides

 

2x - 1  =  ( x-2)^2

 

2x  - 1  =  ( x - 2) ( x - 2)

 

2x - 1  =  x^2  -  4x +  4        subtract  2x from both sides, add 1 to both sides

 

x^2 - 4x - 2x + 4 + 1  = 0

 

x^2 - 6x + 5  =  0     factor

 

(x - 5)  ( x  - 1)  =  0

 

Setting each factor to  0 and solving for x  we get the possible solutions of

 

x = 5    or  x  = 1

 

Note that  x  = 5 solves the original equation   but  x  = 1 doesn't

 

So ... the last answer is correct 

 

 

 

cool cool cool

 Feb 9, 2018
edited by CPhill  Feb 9, 2018

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