MathematicsThe value of positive square root of 2x−3+2×2−3x+2

The value of positive square root of $2 x - 3 + 2 \sqrt{x^{2} - 3 x + 2}$

A
$\sqrt{x - 1} - \sqrt{x - 2}$
B
$\sqrt{x + 1} + \sqrt{x + 2}$
C
$\sqrt{x + 1} - \sqrt{x + 2}$
D
$\sqrt{x - 1} + \sqrt{x - 2}$

Solution:

$\sqrt{2 x - 3 + 2 \sqrt{x^{2} - 3 x + 2}} = \sqrt{2 x - 3 + 2 \sqrt{(x - 2) (x - 1)}}$

$= \sqrt{x - 1} + \sqrt{x - 2}$

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