Got this problem on a test:
12 + √2x-1 = 4
Okay, so then I subtract 12 from both sides:
√2x-1 = -8
2x - 1 = 64 I then square both sides...
2x = 65 Add 1 to each side
x = 65/2 Divide both sides by two.
However, that answer doesn't work. Are there simply no solutions, then?
That is correct, there are no solutions. Not every equation is a true statement. You always check the validity of your answer by plugging into the original equation.
Please go here:
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
That answer is the solution to
-12 + √(2x-1) = -4
When you square you cannot help but introduce 'solutions' to this alternative equation as well so you were right to check the value you had.
Even when you got √2x-1 = -8 you could've said that there are no solutions, because a square root of a positive number is always positive...
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.