Proving x + y is rational
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
35066
Nature and number of solutions to $xy=x+y$
23752
Proving Irrationality
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
158933
Rational solutions of $y^2 = x^3 - x$
96153
$ x^3<y^3 \iff x<y $ proof issue.
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
38851
To find the probability whether $X$ is rational
5595
$x^y = y^x$ for integers $x$ and $y$
126445
Proving the second root of a quadratic equation
98440
Show that any non-negative rational integer may be written as the sum of two squares if it is of the form....
7775
Show that $|x-y|\leq |x|+|y|$.
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
12484
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
148310
Showing rational numbers are algebraic