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Questions  >>  CBSE XI  >>  Math  >>  Mathematical Reasoning
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Q)

Show that the statement "For any real numbers $a$ and $b$, $a^2=b^2$ implies that $a=b$" is not true by giving counter example.

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The given statement is
"For any real numbers $a$ and $b$, $a^2=b^2$ implies that $a=b$"
To show that this statement is false,
Let $a=5$ and $b=-5$
Here $a^2=25$ and $b^2=25$
$i.e.,$ $a^2=b^2$. But $5\neq -5$ $i.e.,$ $a\neq b$
$\therefore$ The given statement is false.
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