Expression 4451

Find the largest natural number d that has that property for any natural number
the number n is the value of the expression

V (n) = n ^ 4 + 11n2−12

is divisible by d.

Correct answer:

d =  12

Step-by-step explanation:

V(n)=n4+11n212 V(n)=n2(n2+11)12 t=n2 t2+11t12=0  t2+11t12=0  a=1;b=11;c=12 D=b24ac=11241(12)=169 D>0  t1,2=2ab±D=211±169 t1,2=211±13 t1,2=5.5±6.5 t1=1 t2=12 V(n)=(n21)(n2+12) = (n1)(n+1)(n2+12) D= { 1,2,3,4,6,12 } d=12

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