Question

Matia claims "When you square any number, the result is always greater than that number." Matia used the example 32 = 9 and 9 is greater than 3

Answer 1

Answers:

Choice A) 0

Choice B) 0.5

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Step-by-step explanation:

Matia claims that
`x^2 > x`

However, the claim isn't true when 0 ≤ x ≤ 1.

For example, x = 0 leads to
`x^2 = 0^2 = 0`

Meaning that
`x^2 > x` would update to
`0 > 0` which is false.

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Similarly, if x = 0.5, then

`x^2 > x\\\\0.5^2 > 0.5\\\\0.25 > 0.5 \ \text{which is also false}\\\\`

Because the last inequality is false, the first inequality must also be false for x = 0.5

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Those last two previous sections showed that x = 0 and x = 0.5 are counter-examples to Matia's claim to thereby prove it false.

Answer 2

`{3}^(2) = 9 \\ \\ 81 = 9`