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What is the smallest real number $x$ in the domain of the function $$g(x) = \sqrt{(x-3)^2-(x-8)^2}~?$$

Guest Jul 11, 2018

#1
+19636
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What is the smallest real number $x$ in the domain of the function $$g(x) = \sqrt{(x-3)^2-(x-8)^2}~?$$

$$\begin{array}{|rcll|} \hline (x-3)^2+(x-8)^2 &=& 0 \\ x^2-6x+9-x^2+16x-64 &=& 0 \\ 10x +9 - 64 &=& 0 \\ 10x - 55 &=& 0 \\ 10x &=& 55 \\ \mathbf{x}& \mathbf{=} & \mathbf{5.5} \\ \hline \end{array}$$

The smallest real number x in the domain of the function is 5.5

heureka  Jul 11, 2018
#1
+19636
+1

What is the smallest real number $x$ in the domain of the function $$g(x) = \sqrt{(x-3)^2-(x-8)^2}~?$$

$$\begin{array}{|rcll|} \hline (x-3)^2+(x-8)^2 &=& 0 \\ x^2-6x+9-x^2+16x-64 &=& 0 \\ 10x +9 - 64 &=& 0 \\ 10x - 55 &=& 0 \\ 10x &=& 55 \\ \mathbf{x}& \mathbf{=} & \mathbf{5.5} \\ \hline \end{array}$$

The smallest real number x in the domain of the function is 5.5

heureka  Jul 11, 2018