ok I have some problems that I need help with:
if a^2 is even, then prove that a is even too
if a^2 is uneven, then prove that a is uneven too
And another problem:
prove that:
rational + irrational number = irrational number
PLS HELP ME!!!
ok I have some problems that I need help with:
if a^2 is even, then prove that a is even too
if a^2 is uneven, then prove that a is uneven too
And another problem:
prove that:
rational + irrational number = irrational number
PLS HELP ME!!!
use the contrapostive
it suffices to show if $\displaystyle a$ is not even, then $\displaystyle a^2$ is not even.
so assume $\displaystyle a$ is not even, so that $\displaystyle a = 2n + 1$ for some integer n, then .....
same approach as aboveif a^2 is uneven, then prove that a is uneven too
by the way, "odd" means "uneven" and it sounds nicer.
Let $\displaystyle \frac ab$ be a rational number and $\displaystyle c$ be an irrational number. what can you say about their sum?And another problem:
prove that:
rational + irrational number = irrational number
PLS HELP ME!!!
Proof:
Let x be an even interger. Then by definition of an even number we can write:
x=2m
where m is an interger.
Therefore x^2= (2m)^2
=4m^2
=2(m^2)
Let P =2m^2. Since the product of integers is an interger, p is an itnerger. Thus x^2 =2p and x^2 is an even integer.
And another problem:
prove that:
rational + irrational number = irrational number
PLS HELP ME!!!I think it would be funny to assume that $\displaystyle \frac ab+c=\frac de$, where $\displaystyle \frac de$ is a rationnal. (a,b,d,e are non-zero integers)Let $\displaystyle \frac ab$ be a rational number and c be an irrational number. what can you say about their sum?
Now, is it logical to say : $\displaystyle \underbrace{c}_{\text{irrational}}=\frac de-\frac ab=\frac{bd-ae}{be}$ ?