Luckily

Algebra Level 4

{ a + 2 b + 3 c = 13 a 2 + 4 b 2 + 9 c 2 + 3 a 2 b + 15 c = 82 \begin{cases} a+2b+3c=13 \\ a^2+4b^2+9c^2 + 3a-2b+15c=82 \end{cases}

Given that a , b a,b and c c are real numbers with a b c a\geq b \geq c and they satisfy the system of equations above, find the value of a a .


The answer is 4.

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2 solutions

Nuttapat Bk
Dec 23, 2015

Aman Joshi
Dec 23, 2015

My was also like this

@Aman Joshi , good job on your first problem! I LOVED it!

A Former Brilliant Member - 3 years, 7 months ago

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Thanks, glad to hear this Lucia

Aman Joshi - 3 years, 7 months ago

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You should make more :) I'm sure you would be famous on Brilliant

A Former Brilliant Member - 3 years, 7 months ago

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@A Former Brilliant Member OK done :p . Being famous.... Thanks but why will I be famous😁

Aman Joshi - 3 years, 7 months ago

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@Aman Joshi thanks! i love problems even though i don't get them usually cuz 6th grade math is as boooooring as Dolores Umbridge (from Harry Potter)

A Former Brilliant Member - 3 years, 7 months ago

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@A Former Brilliant Member U from 6th grade, didn't knew... 😀

Aman Joshi - 3 years, 7 months ago

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@Aman Joshi eh. so is Dobby dumbledore. she is my friend at school. i told her about brilliant ;)

A Former Brilliant Member - 3 years, 7 months ago

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@A Former Brilliant Member Hmm, well nice interaction with you, and read you want to go MIT . Best wishes☺

Aman Joshi - 3 years, 7 months ago

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@Aman Joshi Well i am doing pilot course...... and pen state world campus (even though not supposed to)

A Former Brilliant Member - 3 years, 7 months ago

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@A Former Brilliant Member I am not much aware about them, but its good to have such a mindset during this stage . penn state world campus I suppose is good , quite good. Pleasure to meet you again.

Aman Joshi - 3 years, 7 months ago

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@Aman Joshi eh. thanks u are smart too. very smart

A Former Brilliant Member - 3 years, 7 months ago

@Aman Joshi famous on brilliant, like featured

A Former Brilliant Member - 3 years, 7 months ago

@Aman Joshi , good job 2nd problem! (even though I didnt understand it at all cuz im 11)

A Former Brilliant Member - 3 years, 7 months ago

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