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Which inequality represents all values of x for which the product below is defined?√5x * √x+3A. x>0B. x≤-3C. x≥-3D. x≥0

User Jpvee
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1 Answer

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Having the following product:


(\sqrt[]{5x})\cdot(\sqrt[]{x+3})

We need to establish the values of x for which it is defined.

The product has 2 square roots. We know that square roots are defined in real numbers only when its argument is 0 or a positive number.

We can begin checking the first one: √(5x). The argument of the square root (5x) has to be equal or larger than 0, then:


\begin{gathered} 5x\ge0 \\ \end{gathered}

We can divide both sides by 5, having:


x\ge0

The first factor is defined for values of x larger or equal to 0.

Following the same logic for the other factor:


\begin{gathered} x+3\ge0 \\ x\ge-3 \end{gathered}

Then, we have two restrictions so far:


\begin{gathered} x\ge0 \\ x\ge-3 \end{gathered}

The restrictions for the product of both radicals will be the intersection of the two previous conditions. The first restriction goes from 0 to infinity and the second one from -3 to infinity. The intersection of both intervals gives the numbers from 0 to infinity. Then, the values of x for which the product is defined are:


x\ge0

Correct option is D.

User Keymap
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