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Find all real numbers $k$ such that $|| k (1, 1) - (3, -2) || = \sqrt{37}.$
Ok. Am I supposed to go and manually plug in random number( which sounds terrible) or is there another way?

I could really use some tips to get started. Thank you!

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  • $\begingroup$ Well, what is $||(a,b)||$? $\endgroup$ – lulu Sep 11 '17 at 13:29
  • $\begingroup$ Here's a MathJax tutorial :) $\endgroup$ – Shaun Sep 11 '17 at 13:39
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If you mean by $||(a,b)||=\sqrt{a^2+b^2}$ then :

$$\sqrt{37}=||k(1,1)-(3,-2)||=||(k,k)+(-3+2)||=||(k-3,k+2)||=\sqrt{(k-3)^2+(k+2)^2}$$

Thus $(k-3)^2+(k+2)^2=37$

Continue it from here to find $k$

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