I am given 4 choices for the problem the square root of 8x -2 = the square root of 2x. The choices are a)x=2 or 2/9 b)no solutions c)2/9 or d)x=2.I have imput the numbers and gotten a variety of solutions none of which are any of the choices, does this mean there are no solutions or am I doing this wrong?
square both sides.
64x^2 -32x + 4=2x
64x^2 -30x + 4=0
quadratic formula:
30 +- sqrt (900 -4*64*4) /128
so clearly the problem has a solution. So is the solution real?
sqrt (900 - 1024) = sqrt (-124)
No, the solutions are not real.
Real numbers are in a, c, d. So they are wrong. b if it said NO REAL Solutions would be correct, but it says no solutions, so...
There are no correct answers .
Based on the calculations you provided, it seems that there are no real solutions to the given equation.
To solve the equation √(8x - 2) = √(2x), you squared both sides to eliminate the square roots and obtained the equation 64x^2 - 30x + 4 = 0.
You then used the quadratic formula to find the solutions of the quadratic equation, which yielded 2 complex solutions.
Since the choices only offer real number solutions, it is safe to conclude that none of the given choices are correct.
In this case, the correct answer would be "b) no solutions" if it specified "no real solutions" because there are no real values of x that satisfy the original equation.