It's just square root

Algebra Level 3

$\text{ICE}^3=\sqrt{\text{ICE}^6}$

If $\text{ICE}$ is a real number, state the above equation as true/false.

Clarification: $\text{ICE}$ is one variable. In this problem it is not considered as the product of $\text{I,C}$ and $\text{E}$ .

True False

1 solution

Nihar Mahajan
Feb 17, 2016

If $\color{#3D99F6}{ICE}$ is negative then let $\color{#3D99F6}{ICE}=-\color{#D61F06}{FIRE}$ for some positive real number $\color{#D61F06}{FIRE}$ . Hence ,

$\begin{aligned} \sqrt{\color{#3D99F6}{ICE}^6} &= \sqrt{(-\color{#D61F06}{FIRE})^6} \\ &= \sqrt{(-\color{#D61F06}{FIRE}^3)^2} \\ &=|-\color{#D61F06}{FIRE}^3| \\ &=\color{#D61F06}{FIRE}^3\\ &=-\color{#3D99F6}{ICE}^3 \neq \color{#3D99F6}{ICE}^3 \end{aligned}$

where $i=\sqrt{-1}$ . Clearly , the statement is false when $\color{#3D99F6}{ICE}$ is negative.

Moderator note:

Such a fun solution :)

Nice use of positive $FIRE$ . Great solution!

Sandeep Bhardwaj - 5 years, 3 months ago

I used the fact that $ICE+FIRE=0$ :P Thanks anyways :)

Nihar Mahajan - 5 years, 3 months ago

$\mathfrak{{\color{#D61F06} NICE ONE !}}$

A Former Brilliant Member - 5 years, 3 months ago

$\Large \color{#3D99F6}{\mathcal{CREATIVE!!}}$

Rishabh Jain - 5 years, 3 months ago

$\mathcal{\color{#D61F06}{THANKS!!}}$

Nihar Mahajan - 5 years, 3 months ago

I have no words to extol you answer.

Atanu Ghosh - 5 years, 2 months ago

Nice use of ICE = -FIRE. You even used colors.. Wow!

Abha Vishwakarma - 2 years, 8 months ago

That moment when Luffy solves Math problems

Siddharth Rathore - 5 years, 3 months ago

I am a Luffy in Gear 1729. So I am intellectually strong as well ;)

Nihar Mahajan - 5 years, 3 months ago

It's just square root

1 solution

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