If two numbers represented 2m+1 and 2m+5 have a sum of 74 find m
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Answer:
Step-by-step explanation:
Firstly, you need to know that raising a fraction to a power raises both the top and the bottom to that power.
Second, a negative power on the top and bottom flips the fraction
Last, raising a power to a power multiplies the powers
So, =
=
=
You can find counterexamples to disprove this claim. We have positive integers that are perfect square numbers; when we take the square root of those numbers, we get an integer.
For example, the square root of 1 is 1, which is an integer. So if y = 1, then the denominator becomes an integer and thus we get a quotient of two integers (since x is also defined to be an integer), the definition of a rational number.
Example: x = 2, y = 1 ends up with which is rational. This goes against the claim that
is always irrational for positive integers x and y.
Any integer y that is a perfect square will work to disprove this claim, e.g. y = 1, y = 4, y= 9, y = 16. So it is not always irrational.