Question

which graph represents the solution set of x^(2)-2>0?

Answer 1

\[\large{x^2-2>0}\]
\[\large{\implies x^2 > 2}\]


Now, remember this:

\[\large{\text{if}~~ y^2 = a^2}\]
\[\large{\text{then}~~ |y| = a}\]

Thus,

\[\large{x^2 > 2}\]
\[\large{\implies|x| > \sqrt{2}}\]
\[\large{\implies x > \sqrt{2}~~\text{or}~~ x < -\sqrt{2}}\]



Shaded region represent the inequality.