The value of positive square root of 2x−3+2x2−3x+2

$$2x$$−$$3+2x2$$−$$3x+2=2x$$−$$3+2(x$$−$$2)(x$$−$$1)=x$$−$$1+x$$−$$2$$

Q.

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

Moderate

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

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

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

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

answer is D.

(Detailed Solution Below)

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Detailed 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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