Answer:
x = 1
Step-by-step explanation:
The graph is shown below. The solution is x = 1.
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√x +2 = 3x . . . . given
√x = 3x -2 . . . . . subtract 2
x = 9x^2 -12x +4 . . . . square both sides
9x^2 -13x +4 = 0 . . . . subtract x to put in standard form
(x -1)(9x -4) = 0 . . . . . factor the quadratic
x = 1 . . . or . . . x = 4/9 . . . . values of x that make the factors zero
The "solution" x = 4/9 is extraneous, in that it does not satisfy the equation. It would correspond to the intersection of the line with the negative branch of the square root function. That is, it does satisfy -√x +2 = 3x.
The solution is x=1.
