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\(Find all solutions to $\sqrt{x} + \sqrt{x + 6} = 6.$ \)

 Apr 20, 2019
 #1
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√x  + √[ x + 6 ]  =  6      subtract √x from both sides

 

√ [x + 6 ]  =  6 - √x       square both sides

 

x + 6  =    36  -12√x  + x       subtract x from both sides

 

6 = 36 - 12√x      rearrange as

 

12√x  = 36 - 6

 

12√x =  30       divide both sides by 12

 

√x =  30/ 12    =  5/2      square both sides again

 

x  =  (5/2)^2  = 25 / 4

 

 

cool cool cool

 Apr 20, 2019

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