# Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set - Page 668: 24

no solution

#### Work Step by Step

Using the properties of equality, the given equation, $3x^{1/2}+12=9$, is equivalent to \begin{array}{l} 3x^{1/2}=9-12 \\\\ 3x^{1/2}=-3 \\\\ x^{1/2}=-\dfrac{3}{3} \\\\ x^{1/2}=-1 .\end{array} For any real number, the left side of the equal sign, $x^{1/2}$, always gives a positive number. This will never be equal to the negative expression on the right of the equal sign. Hence, there is $\text{ no solution.}$

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