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ESTION 1 Given: \( T=\frac{\sqrt{x+5}}{x-1} \), where \( x \in\{-6 ;-2 ; 1 ; 4\} \). Choose from the given set of numbers a value of \( x \) for which \( T \) will be: 1.I.1 rational 1.1.2 non-real

Ask by Fuentes Byrd. in South Africa
Mar 15,2025

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For \( x = 4 \), \( T \) is rational. For \( x = -6 \), \( T \) is non-real.

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To find a value of \( x \) for which \( T \) is rational, we can test the provided values. For \( x = 4 \): \[ T = \frac{\sqrt{4+5}}{4-1} = \frac{\sqrt{9}}{3} = \frac{3}{3} = 1 \quad \text{(rational)} \] For \( x = 1 \): \[ T = \frac{\sqrt{1+5}}{1-1} = \frac{\sqrt{6}}{0} \quad \text{(non-real, as division by zero is undefined)} \] Thus, if you choose \( x = 4 \), \( T \) is rational, and if you choose \( x = 1 \), \( T \) is non-real. Testing values is important, as sometimes the obvious choice isn't the logical one. For instance, the division by zero is a common mistake many make - always check if your denominator could zero out! If you're intrigued by how mathematical functions behave, consider exploring more on rational expressions and their properties. There are some really fun and engaging resources like video tutorials or books that explain similar concepts with interactive problems. Math doesn't need to be boring; dive in and discover the excitement!

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