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Show that the statement For any real num...

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

Text Solution

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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
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Knowledge Check

  • For any whole numbers a, b, c is it true that (a+b)+c=a+(c+b) ? Give reasons.

    A
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    D
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    A
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    B
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