You don't need to know how to solve it. You only need to know how to tell if a given value of x is a solution.

Testing the first of the possible answers (x=3) gives

.. √(4*3 -3) = 2 +√(2*3 -5)

.. √9 = 2 +√1

.. 3 = 2 +1 . . . . solution checks OK

This is the only answer containing x=3, so

.. A is the selection of choice.

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A graphing calculator can also be helpful. It is usually easiest to cast the problem as

.. f(x) = 0

Here, we have subtracted the right side of the equation to make it

.. √(4x -3) -(2 +√(2x -5)) = 0

The graph has x-intercepts at x=3 and x=7. (see source link)

4x - 3 = 4 + (2x - 5) + 4 √ (2x - 5)

2x - 2 = 4 √ (2x - 5)

4x² - 8x + 4 = 16 [ 2x - 5 ]

4x² - 40 x + 84 = 0

x² - 10x + 21 = 0

[ x - 7 ] [ x - 3 ] = 0

x = 3 , x = 7

sqrt(4x - 3) = 2 + sqrt(2x - 5)

Square both sides, then simplify the RHS. Beware: the square root will still be there!

4x - 3 = 4 + 4 sqrt(2x - 5) + (2x - 5)

4x - 3 = 2x - 1 + 4 sqrt(2x - 5)

Subtract 2x from both sides, then add 1 to both sides:

2x - 3 = -1 + 4 sqrt(2x - 5)

2x - 2 = 4 sqrt(2x - 5)

Divide everywhere by 4 and simplify the LHS:

(2x - 2) / 4 = sqrt(2x - 5)

(x - 1) / 2 = sqrt(2x - 5)

Square both sides again:

(x^2 - 2x + 1) / 4 = 2x - 5

Multiply everywhere by 4:

x^2 - 2x + 1 = 8x - 20

Subtract 8x and add 20 to both sides:

x^2 - 10x + 1 = -20

x^2 - 10x + 21 = 0

Factor the LHS:

(x - 3)(x - 7) = 0.

Set each factor to 0 and x = 3 or 7. Both answers are valid; the answer is A).

The radicands must be non-negative, so

2x-5 ≥ 0

x ≥ 2.5

There is only one solution for which both values of x are greater than 2.5