If x = 2 and y = -3, what is the value of 2x^2 + 3xy – 2y^2?
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Answer:
Step-by-step explanation:
A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.
To write a ratio, we count the number of each quantity we are comparing or use the variable for that quantity. We write radius:circumference. Recall, the circumference of a circle can be found using or
.
We write r: or r:
.
We can also write in fraction form:
or
When , we have
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for , that
Now for , we have
so we know the left side is at least divisible by by our assumption.
It remains to show that
which is easily done with Fermat's little theorem. It says
where is prime and
is any integer. Then for any positive integer
,
Furthermore,
which goes all the way down to
So, we find that
QED