The product of all the rational roots of the equation (x^2-9 x+11 )^2-(x-4)(x-5)=3 , is equal to

Step-by-step solution

aligned & (x^2-9 x+11 )^2-(x-4)(x-5)=3 & (x^2-9 x+11 )^2- (x^2-9 x+20 )=3 aligned Let x^2-9 x+11=t aligned & t^2-(t+9)=3 & t^2-t-12=0 & t^2-4 t+3 t-12=0 & t(t-4)+3(t-4)=0 & t=4 or -3 & x^2-9 x+11=4 & x^2-9 x+7=0 aligned Here, we will get irrational roots aligned & x^2-9 x+11=-3 & x^2-9 x+14=0 & x^2-7 x-2 x+14=0 & x=7,2 & Product of all rational roots =14 aligned