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