If n is an integer, then which of the following statements is/are FALSE?
If n is an integer, then which of the following statements is/are FALSE?
I)n^3 – n is always even.
II)8n^3 +12n^2 +6n +1 is always even.
III)√ (4n^2 – 4n +1) is always odd.
Answer/Solution
II only
Steps/Work
1) n^3 – n
n^2(n-1)
two cases
if n=odd then n-1 is even thus n^2(n-1) is even
if n=even then n^2 is even thus n^2(n-1) is even------>true for all cases
2) 8n^3 +12n^2 +6n +1
8n^3 +12n^2 +6n=Even
but Even +1 =odd------------>Always False
3) for this i tried picking number upto 15 and find all cases True------>True
However will be looking for any algebraic solution
Ans B
n^2(n-1)
two cases
if n=odd then n-1 is even thus n^2(n-1) is even
if n=even then n^2 is even thus n^2(n-1) is even------>true for all cases
2) 8n^3 +12n^2 +6n +1
8n^3 +12n^2 +6n=Even
but Even +1 =odd------------>Always False
3) for this i tried picking number upto 15 and find all cases True------>True
However will be looking for any algebraic solution
Ans B