Math also Fails! -1

Let's play with some numbers for a while with our mathematical tools and let's see what we get

Lets take $7$ and $11$

As you will agree with the identity $(a-b)^2=(b-a)^2$

$(7-11)^2=(11-7)^2$

As you shall agree if $a^2 = b^2$ then $a=b$

$7-11=11-7$

Adding both side by $11$ and $7$

$2(7)=2(11)$

$\boxed{7=11}$

Now will you agree with this? Didn't this means Math also fails!

#NumberTheory

Easy Math Editor

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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}`	$\boxed{123}$

Comments

Why this happened?

It is because of the wrong convention that if $a^2=b^2$ then $a=b$

For example : $2≠-2$ but $2^2= (-2)^2$

If you consider $a^2=b^2$ $a^2-b^2=0$ $(a-b)(a+b)=0$ $\therefore a=b,a=-b$ Hence it is not necessary always that if $a^2=b^2$ then $a=b$ it can be $a=-b$

Now you may have understood what is going on here.

Zakir Husain - 1 year ago

Also while taking square roots you need to put a plus minus sign in front of it so that we don't run into a contradiction.

Aruna Yumlembam - 1 year ago

The value of √4 will be 2 or +/-2

A Former Brilliant Member - 11 months, 3 weeks ago

As you shall agree if $a^2 =b^2$ then $a=b$ .

This condition is not necessarily true.

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}`	$\boxed{123}$