Show that the statement For any real numbers `a\ a n d\ b ,\ a^2=b^2` implies that `a=b` is not true by giving a counter example

Explanation

Let a = 2 and b = – 2, then a and b are real numbers and

`a^2 = b^2 `

`∵ a^2 = (2)^2 = 4, `

`b^2 = (-2)^2 = 4 `

`a^2 = b^2` but a ≠ b (∵ 2 ≠ – 2)

Hence, a,b ∈ R and
` a^2 = b^2 ⇒ a = b `is not true