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 Brilliant Member
5 years, 3 months 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 - 5 years, 3 months ago

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But...it 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...

Brilliant Member - 5 years, 3 months ago

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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 - 5 years, 3 months ago

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

Brilliant Member - 5 years, 3 months ago

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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 - 4 years, 10 months ago

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