iohanetc

2021-02-13

Confirm that if x is rational and $x\ne 0$ , then $\frac{1}{x}$ is rational.

insonsipthinye

Skilled2021-02-14Added 83 answers

Given:

x is rational

$x\ne 0$

TO PROOF:$\frac{1}{x}$ is rational

DIRECT PROOF

Property rational numbers:

if a is a rational number, then there exists two integers y and z such that

$a=\frac{y}{z}(withz\ne 0)$ .

x is an rational number and thus there exists integers y and z such that:

$x=\frac{y}{z}$

Since$x-0$ , we then also know that the numerator cannot be zero

$y\ne 0$

We are interesred in$\frac{1}{x}$ :

$\frac{1}{x}=\frac{1}{\frac{y}{z}}=\frac{z}{/}y$

Since z and y are integers(with$y\ne 0$ ), we then know that $\frac{1}{x}$ is rational.

Result: if x is rational and$x\ne 0$ , then $\frac{1}{x}$ is rational.

x is rational

TO PROOF:

DIRECT PROOF

Property rational numbers:

if a is a rational number, then there exists two integers y and z such that

x is an rational number and thus there exists integers y and z such that:

Since

We are interesred in

Since z and y are integers(with

Result: if x is rational and

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$