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.
+129881 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
