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# Distance formula

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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
+2453
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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
+13894
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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.

!

Apr 24, 2022