Explanation

(c)
$\because\ \sqrt{5x^{2} - 8x + 3} - \sqrt{5x^{2} - 9x + 4} = \sqrt{2x^{2} - 2x} - \sqrt{2x^{2} - 3x + 1}$
Also, $\left( 5x^{2} - 8x + 3 \right) - \left( 5x^{2} - 9x + 4 \right) = \left( 2x^{2} - 2x \right) - (2x^{2} - 3x + 1)$
$\Rightarrow \ x - 1 = x - 1$
$\Rightarrow \ x = 1$ is the required value.