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# Help!!

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

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

Jul 30, 2022
edited by CPhill  Jul 30, 2022