If limx→∞xαx2+x4+1-2x exists and has value non-zero finite real number L, then the value of 100-αL2 is

we have limx→∞ xαx2+x4+1−2x2x2+x4+11/2+2x=limx→∞ xαx4+1−x2x2+x4+11/2+2x=limx→∞ xα+11+1x4−11+1x4+11/2+2=122limx→∞ xα+11+12⋅1x4+…−1So, for above limit to exist and has value non-zero, we must haveα+1=4⇒α=3 and L=122×12=142⇒L2=132