The number of integral roots of the equation $x^4+\sqrt{x^4+20}=22$, is _____.

2

Putting $x^4 = t$ in the given equation, we get $t+\sqrt{t+20}=22$ $⇒t +20=(22-t)^2$ $⇒t^2-45t + 464 = 0$ $⇒(t-16)(t-29)=0$ $⇒t=16,9$ $⇒x^4=16, x^4 =9⇒ x=±2$    [∵ x is an integer]