Problem 1) √4 - x = -2
x -2 x -2
Problem 2) √x + 2 - x = 0
Was confused on the answers; please re-advise
Problem 1) √4 - x = -2
x -2 x -2
Problem 2) √x + 2 - x = 0
Was confused on the answers; please re-advise
sqrt(4) = 2.
For 2 - x/(x-2) = -2/(x-2) start by multiplying through by (x-2) to get the variable out of the denominator. This gives:
2*(x-2) - x = -2. Expand this out, then combine the constant terms on one side and variable terms on the other.
2*x - 2*2 - x = -2
2*x - x = 4 - 2 Factor out the coefficients in front of x
(2-1)*x = 2 Divide to isolate x
x = 2
If you set x = 2 in the original equation, the result is to divide by 0 so it is not a valid solution.
For sqrt(x) + 2 - x = 0, I like to do this with a substitution by defining another variable y = sqrt(x).
The new equation becomes
y + 2 - y^{2} = 0, multiply by -1
y^{2} -y - 2 = 0
(y-2)(y+1) = 0
y = 2, -1
Since y = sqrt(x), x = y^2, so:
x = 4, 1
However, plugging these back into the original equation shows that only x =4 is a valid solution. This is because the sqrt(x) cannot equal (-1).