Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
The sum of rational and irrational numbers will always be an irrational number. It can be proved by the method of contradiction.
Consider a rational number 'u/v' and an irrational number 'a'. Let assume the sum of these numbers is a rational number 'x/y'. If our assumption is wrong, there will be some contradiction while proceeding further.
From the above expression.
Here, 'x/y' and 'u/v' are assumed to be rational number. Thus, 'x', 'y', 'u', and 'v' are integers.
The product of two integers is an integer.
The difference between the two integers is also an integer.
And finally, the ratio of two integers is a rational number. Thus, expression (1) can not be accurate.
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