Question 145
Let us recall that the numbers $\sqrt{2}$, $\sqrt{3}$, and $\sqrt{6}$ are irrational.
(1)
For all integers $s, t$, and $r$, if $s + \sqrt{2} t + \sqrt{3} r = 0$, then prove that $s = t = r = 0$.
(2)
For all integers $a, b, c$, and $d$, if the ratio $\frac{a + \sqrt{2} b + \sqrt{3} c}{b + \sqrt{2} c + \sqrt{3} d}$ is a rational number, then prove that $ad = bc$.
(Nursoltan Khavalbolot)
(1)
For all integers $s, t$, and $r$, if $s + \sqrt{2} t + \sqrt{3} r = 0$, then prove that $s = t = r = 0$.
(2)
For all integers $a, b, c$, and $d$, if the ratio $\frac{a + \sqrt{2} b + \sqrt{3} c}{b + \sqrt{2} c + \sqrt{3} d}$ is a rational number, then prove that $ad = bc$.
(Nursoltan Khavalbolot)