If cos2⁡π8 is a root of the equation x2+ax+b=0 where a, b,∈Q, then the least value of the expression x2+8bx+a is __________.

cos⁡π4=2cos2⁡π8−1⇒cos2⁡π8=12+112⇒cos4⁡π8=1412+1+22=32+214⇒1432+2+a212+1+b=0⇒38+a2+b+214+a4=0Since a and b are rational,14+a4=0,38+a2+b=0⇒ a=−1,b=18∴ x2+8bx+a=x2+x−1=(x+1/2)2−5/4So, required least value is -5/4.