Prove that for every pair of integers m and n, if n − m is even, then n 2 − m is also even. (You may freely use the fact that th
1 answer:
Answer with Step-by-step explanation:
We are given that n and m are two integers
We have to prove that if n-m is even , then is also even.
We know that sum of two odd numbers is even.Sum of an odd number and even number is odd.
Product of an odd number and even number is even.
Case 1.Suppose m and n are both even n=4 , m=2
Case 2.Suppose m odd and n odd
n=9,m=5
Hence, proved.
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Answer:
You can proceed as follows:
Step-by-step explanation:
First solve the quadratic inequality . To do that, factorize, then we have that
. This implies that
or
In the first case the solution is the empty set . In the second case the solution is the interval
. Now we have that
.
To show that consider
. Then
, this implies that
, then
. Now, to show that
consider
, then
, then
, then
, this implies that
.
Observe the image below.
9514 1404 393
Explanation:
sum -- the result of addition: 5x+1
term -- a constant, variable, or product of a constant and one or more variables. In the more general sense, a term is any part of the expression that can be considered by itself. An example is 5x
product -- the result of multiplication: 9(5x+1), where 9 is multiplied by the sum (5x+1)
factor -- part of a product: x
quotient -- the result of division: 9(5x+1)÷3
coefficient -- a constant, or the constant that multiplies the variables in a term: 5
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<em>Additional comment</em>
The way this is written, there will be the tendency to think of 3y as a term in the same sense that 5x is a term. That would be incorrect. The Order of Operations has you interpret this expression as ...