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by multiplying both sides of the equation by x^1/2 and using a suitable substitution solve:

2x^1/2=12x^(-1/2)-5

 Apr 15, 2022
 #1
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2x^(1/2)  = 12 / x^(1/2)  - 5                multiplying through by x^(1/2)    we get

 

2x = 12 - 5x^(1/2)

 

2x - 12  =  - 5x^(1/2)           square both sides

 

4x^2 - 48x + 144  =  25x

 

4x^2 - 73x + 144  = 0        factor  as

 

(4 x - 9) ( x - 16)  = 0

 

Setting both factors to 0  and  solving for  x we get that

 

x = 9/4   or  x  =16

 

Which is true  ????

 

If x = 9/4  then x^(1/2)  = 3/2

 

2 (3/2) =  12 / (3/2) - 5

3  =  8 - 5       true

 

If x = 16  then x^(1/2)  = 4

 

2(4)  = 12 / 4 - 5

8 = 3 - 5    not  true

 

The answer is   x =   9/4

 

We get the extraneous answer  of x =16  because of squaring......this often happens   !!!!

 

cool cool cool

 Apr 15, 2022

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