The number of irrational roots of the equation4x−1x2+8x+1x=29 is

Put x + 1/x = t to obtain4t2−4+8t=29  or  4t2+8t−45=0⇒t2+2t=454⇒(t+1)2=454+1=722⇒t=−1±72=−92,52Thus, x+1x=−92,52⇒ x2+92x+1=0, x2−52x+1=0The first equation has irrational roots and the second equation has rational roots