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.

Guest Jul 30, 2022

#1**+1 **

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

CPhill Jul 30, 2022