Math problems from competitions

Hello! I would like to ask some maths problems here.:-)

1) How to prove that any triangle can be cut into six similar triangles? (Your proof must be valid for all triangles and not just a specific type. )

2) Given that real number a,b,ca, b, c where abc=1,a+b+c=4abc=-1, a+b+c=4

a(a23a1)+a(b23b1)+a(c23c1)=49\frac {a}{(a^2-3a-1)}+\frac {a}{(b^2-3b-1)}+\frac {a}{(c^2-3c-1)}=\frac {4}{9}

Thus, find a2+b2+c2=a^2+b^2+c^2=

These problems may be easy for you, but I hope you can explain the working/solution as a reply below:-D. Thanks!

There's still some maths problems...maybe in the next note!

*See part 2 here

Note by A Former Brilliant Member
6 years ago

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Hi, Plz are you sure of ur second question,,, Seems there needs to be cyclic terms in numerator, Plz can u edit it

Dinesh Chavan - 6 years ago

Log in to reply is from the competition question...but can you tell me what's wrong in that question and I'm not so sure about cyclic terms...

How about the first question? I tried it, but I still cannot find a way to proof it...

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I Mean see the terms in the inequality,, a's on 1st term, b's on second term, c's on 3rd one. I mean to say, normally these inequalities are symetric type. I think u might have mae a mistake while copying . U might have not seen numerator clearly. Just in case, plz clarify it.. While, I will try now :P

Dinesh Chavan - 6 years ago

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@Dinesh Chavan Ok.The question is really printed like that...:-(

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I've solved #2 but I'm having a hard time with the first one can anyone help me?

brittany gutknecht - 5 years, 8 months ago

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