Answer:
Proof given by contradiction.
Step-by-step explanation:
Given that:
To prove:
is prime if and only if no positive integer > 1 and divides .
Solution:
First of all, let is a composite number i.e. not a prime number such that:
and and are prime and divides and also divides .
Let
or
1. :
is prime and is a divisor of .
2. :
We have assumed that
is a prime number and is a divisor of .
But we are given that no prime number divides but we have proved that divides .
So, it is a contradiction to our assumption.
Therefore, our assumption is wrong that is a composite number.
Hence, proved that is a prime number.
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Answer:
13/35
Step-by-step explanation:
13 students choose football.
31 students choose tennis.
this leaves 26 students that chose running.
probability of choosing running is 26/70 = 13/35
Assuming you are speaking of the Real Numbers…
x^2+66=14x+15
x^2 - 14x + ?? = -51
x^2 - 14x + (half of -14 squared) = -51 + (half of -14 squared)
x^2 - 14x + 49 = -51 + 49
(x - 7)^2 = -2
By the way, in the real number system, you can’t square any number and get a negative so the above equation has no solution. If you allowed for complex solutions…there would be two of those.
12 + 4(5) = 12 + 4(5)
12 + 20 = 12 + 20
32 = 32