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Solve each equation. Check each solution. if there is no solution, type "no solution."
\(\sqrt{10x-17} - \sqrt{5x-102} = 0\)


Could someone please tell me what the answer to this is?

I have already found the value of x and the supposed solution is -17. However, when I plug in -17, the equation becomes \(\sqrt{-187} - \sqrt{-187} = 0\). Technically, anything subtracted by itself should equal 0, but because they are imaginary numbers, I'm not sure if the answer is actually no solutions. When I put in the equation into an algebra calculator, I keep getting no solutions.

 Jul 30, 2022
 #1
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Rearrange as

 

sqrt (10x -17)  = sqrt (5x - 102)     square both sides

 

10x  -  17 =   5x  -102

 

10x  -5x  =  -102 + 17

 

5x  =  -85

 

x = -85/ 5  =  -17

 

Note that

 

10 (-17) - 17 = - 187

And

5(-17) - 102 =  -187

 

So  x = -17  is the  solution (assuming that complex forms  are OK )  and we actually have

 

sqrt ( -187) - sqrt (-187)  = 0

 

sqrt (187) i  -  sqrt (187) i  =  0

 

 i ( sqrt (187) - sqrt (187) )  = 0

 

i (0)  = 0   

 

0i = 0   

 

0 = 0   is true

 

 

 

cool cool cool

 Jul 30, 2022
edited by CPhill  Jul 30, 2022

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