En un día laboral determinado, Saranne archiva el 50% de la
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Gaming a video-game designer is using the expression 6n3 in a program to determine points earned, where n is the game level.
Given expression is . the given expression is for the nth level.
To simplify the expression for the level, we plug in
in the place of 'n' in the given expression
(multiply the exponents)
Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that
was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.