(1) A rational number is any real number of the form (p)/(q) where p, q are integers. Use a dire

Step 1: Assume that r and s are rational numbers.

Question

(1) A rational number is any real number of the form $\frac{p}{q}$ where $p$, $q$ are integers. Use a direct proof to show that if $r$ and $s$ are rational numbers, then $r + s$ is also rational. (2) A perfect cube is any integer of the form $a^3$ where $a$ is an integer. Show that if $9 \le x \le 26$ is a perfect cube, then $x$ is divisible by 4. (Hint: What type of proof is applicable here?) (3) Let $x$ be a real number. Show that if $x > 3$, then $\frac{1}{x^2 + 2} < 1$. (Hint: what type of proof is applicable here?)

          (1) A rational number is any real number of the form $\frac{p}{q}$ where $p$, $q$ are integers. Use a direct proof to show that if $r$ and $s$ are rational numbers, then $r + s$ is also rational.
(2) A perfect cube is any integer of the form $a^3$ where $a$ is an integer. Show that if $9 \le x \le 26$ is a perfect cube, then $x$ is divisible by 4. (Hint: What type of proof is applicable here?)
(3) Let $x$ be a real number. Show that if $x > 3$, then $\frac{1}{x^2 + 2} < 1$. (Hint: what type of proof is applicable here?)

(1) A rational number is any real number of the form (p)/(q) where p, q are integers. Use a direct proof to show that if r and s are rational numbers, then r + s is also rational.
(2) A perfect cube is any integer of the form a^3 where a is an integer. Show that if 9 ≤ x ≤ 26 is a perfect cube, then x is divisible by 4. (Hint: What type of proof is applicable here?)
(3) Let x be a real number. Show that if x > 3, then (1)/(x^2 + 2) < 1. (Hint: what type of proof is applicable here?)

Added by Carla M.

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