2. Given $t>0$, for the equation $|x|+\sqrt{t-x^{2}}=\sqrt{2}$, the number of distinct real roots of this equation is . $\qquad$
2. 0 or 2 or 3 or 4 Detailed Explanation: Let $C_{1}: y=|x|-\sqrt{2}, C_{2}: y=-\sqrt{t-x^{2}}$, using the combination of numerical and graphical methods, we know: When $02$, the equation has no real roots; When $t=1$, the equation has 2 real roots; When $t=2$, the equation has 3 real roots; When $1<t<2$, the equation has 4 real roots.