(x2−9x+11)2−(x−4)(x−5)=3 (x2−9x+11)2−(x2−9x+20)=3 Let x2−9x+11=t t2−(t+9)=3 ⇒t2−t−12=0 ⇒t2−4t+3t−12=0 ⇒t(t−4)+3(t−4)=0 ⇒t=4 or −3 x2−9x+11=4 x2−9x+7=0 Here, we will get irrational roots x2−9x+11=−3 x2−9x+14=0 x2−7x−2x+14=0 ⇒x=7,2 ⇒ Product of all rational roots =14
