Let a = $\sqrt(52)$, b = $\sqrt(50)$ and c = $\sqrt(2)$.
Without finding their actual values, is it possible to prove that
a + b > c
a + c > b
b + c > a
This is part of a coordinate geometry problem where we are asked to prove that 3 points form a triangle
#Proving inequality of 3 surds without finding their values.
pure marsh
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devooko
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Let a = $\sqrt(52)$, b = $\sqrt(50)$ and c = $\sqrt(2)$.
Without finding their a...
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pure marsh
yes
hollow tartan
a+b > c and a+c > b should be simple enough, as a>b>c
pure marsh
wait one min I have one other doubt, isnt it enough to prove that the points are not collinear to show that they form a triangle ?
hollow tartan
for b+c>a, square both sides and collect like terms
hollow tartan
wait one min I have one other doubt, isnt it enough to prove that the points are...
yes, but these are side lengths and not points
pure marsh
I mean when points are given
hollow tartan
triangle inequality
(on a side note: i was going to tell you that they formed a right triangle as per Pythagoras’ theorem)
pure marsh
yes, I know, but before that we have to prove that it is indeed a triangle right ? We cant just directly write "since a^2 + b^2 = c^2, the points form a right triangle" right ?
hollow tartan
this was before i realized that the question required a proof of them forming a triangle
hollow tartan
for b+c>a, square both sides and collect like terms
have you tried this?
hollow tartan
I mean when points are given
yes
pure marsh
wait lemme try
Um actually I havent learned inequalities just yet, but I would like to learn. Could you expand on what you mean by "for b+c>a, square both sides and collect like terms"
wait never mind got it, so we assume that it is greater, then square, then arrive at a true statement, then we conclude that the original inequality is true.
Wow, thank you sir, I asked this to my maths teacher but she just told me to do it like in the textbook.
Much appreciate it, may god bless you 🙂
hollow tartan
wait never mind got it, so we assume that it is greater, then square, then arriv...
technically, we should prove that (rt(50)+rt(2))^2 > 52 first, and then square root both sides
because making assumptions is quite hard to do properly
worldly raptorBOT
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@pure marsh