This can't be proved because it is not necessarily true.
If x is 2 and y is 1 then x-y is 1, which is rational.
The product of 2x and 3y is 12, which is also rational.
Sadly, you can't disprove it either; for certain values of x,y it is true as posited.
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1) Adding an irrational number and a rational number will always give you an irrational number. 2) Multiplying an irrational number by a non-zero rational number will always give you an irrational number.
No. The number pi is irrational, and if you multiply an irrational number by a non-zero rational number (in this case, -2), you will get another irrational number.As a general guideline, most calculations that involve irrational numbers will again give you an irrational number.
ANY number with a finite number of decimal digits is RATIONAL.(Also, numbers with an infinite number of decimals may be rational - in which case the digits repeat - or irrational.)
Suppose A = 2 + sqrt(3) and B = 5 - sqrt(3) Then A and B are two irrational numbers but A + B = 2 + sqrt(3) + 5 - sqrt(3) = 7 which is rational.
1 + pi, 1 - pi. Their sum is 2.