That is obviously true, right?

Algebra Level 1

$\begin{aligned} \color{#20A900}{a^2}=&\color{#3D99F6}{b^2} \\ \implies \color{#20A900}{a}=&\color{#3D99F6}{b} \end{aligned}$

Is the above statement true?

Yes No

2 solutions

Colin Carmody
Feb 28, 2016

If A is -2 and B is 2, it doesn't work. (They have to be both positive or both negative of the same absolute value)

Bonus Question: Is the converse $\left( a=b \Rightarrow a^2 =b^2 \right)$ true?

Sandeep Bhardwaj - 5 years, 3 months ago

Yes, the converse is true. As $x\,=y\,$ implies $x$ and $y$ are equal ( both in magnitude and sign ), so their squares are equal.

Aditya Sky - 5 years, 3 months ago

Kay Xspre
Feb 28, 2016

Not true. If you factorize the second equation it will be $(a-b)(a+b) = 0\Rightarrow a = ±b$