Recurring Proof Note $7$

I'll prove that:

$y = x_1. \overline{x_2} =$ $\frac{x_1x_2 - x_1}{9}$

Let:

$y = x_1.\overline{x_2}$

$10y = x_1x_2.\overline{x_2}$

$10y - y = 9y$

$x_1x_2.\overline{x_2} - x_1.\overline{x_2} = x_1x_2 - x_1$

$9y = x_1x_2 - x_1$

$\frac{9y}{9}$ $=$ $\frac{x_1x_2 - x_1}{9}$

$y =$ $\frac{x_1x_2 - x_1}{9}$

Therefore, $y = x_1. \overline{x_2} =$ $\frac{x_1x_2 - x_1}{9}$

#Algebra

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Comments

Can you explain what are $x_1 and \overline{x_2}$ ?

A Former Brilliant Member - 11 months, 2 weeks ago

$x_1, x_2$ are variables that denote any number. $\overline{0}$ denotes the recurring symbol.

Yajat Shamji - 11 months, 2 weeks ago

Can you give me an example?

A Former Brilliant Member - 11 months, 2 weeks ago

@A Former Brilliant Member – Let:

$y = 1.\overline{3}$

$10y = 13.\overline{3}$

$10y - y = 9y$

$13.\overline{3} - 1.\overline{3} = 12$

$9y = 12$

$\frac{9y}{9}$ $=$ $\frac{12}{9}$

$y =$ $\frac{12}{9}$

$y =$ $\frac{4}{3}$

Yajat Shamji - 11 months, 2 weeks ago

@A Former Brilliant Member – In this case $x_1 = 1, x_2 = 3, \overline{x_2} = \overline{3}$ .

Yajat Shamji - 11 months, 2 weeks ago

@Yajat Shamji – Ok. I got it, thank you!

A Former Brilliant Member - 11 months, 2 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Recurring Proof Note \(7\)

Comments