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The distance between the points (x, 21) and (4, -7) is \(16 \sqrt{2}\). Find the sum of all possible values of x.

 Apr 24, 2022
 #1
avatar+1370 
+2

This problem isn't possible. The shortest possible line segment would be between \((4, -7)\) and \((4, 21)\).

 

This line segment has a length of 28, which is greater than \(16 \sqrt2\), so there are no points that work. 

 Apr 24, 2022
 #2
avatar+13577 
+1

Find the sum of all possible values of x.

 

Hello Guest!

 

\(y=\sqrt{(16\sqrt{2})^2-(x-4)^2}-7\\ y=21\\ 21=\sqrt{512-(4-x)^2}-7\\ 28^2=512-16+8x-x^2\)

\(x^2-8x+286=0\\ x=4\pm\sqrt{16-286}\\ x=4\pm 3i\sqrt{30}\)

\(x\ne\mathbb R\) | No solution.

laugh  !

 Apr 24, 2022

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