State true or false by giving suitable example if $x$ and $y$ are rational numbers such that $x^2=y^2$

Given:  Statement: "if $x$ and $y$ are rational numbers such that $x^2=y^2$, then $x$ is always equal to $y$".

 To do: To check whether the given statement is true or false with an example.

Solution:

As given, $x^2=y^2$

$\Rightarrow \sqrt{x^2}=\sqrt{y^2}$

$\Rightarrow x=y$

Let $x=4\ \Rightarrow y=4$, 

$\Rightarrow x^2=4^2=16$

$\Rightarrow y^2=4^2=16=y^2$

Thus, The statement: "if $x$ and $y$ are rational numbers such that $x^2=y^2$, then $x$ is always equal to $y$" is true

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Updated on: 10-Oct-2022

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