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Find abc !

Note by Raju Pratama
2 years, 5 months ago

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First off, notice that \( b^{-1} = ac , a^{-1} = bc, c^{-1} = ab \).

Then,

\( \dfrac{1}{a + b^{-1} + 1} = \dfrac{1}{a + ac + 1} \)

\( \dfrac{1}{b + c^{-1} + 1} = \dfrac{1}{b + ab + 1} = \dfrac{abc}{b + ab + abc} = \dfrac{ac}{1+a+ac}\)

\( \dfrac{1}{c + a^{-1} + 1} = \dfrac{1}{c + bc + 1} = \dfrac{abc}{c+cb + abc} = \dfrac{ab}{1+b+ab} = \dfrac{ab}{abc + b + ab} = \dfrac{a}{1+ a + ac} \)

Add them all up and you'll get the answer.

Siddhartha Srivastava - 2 years, 5 months ago

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thank's very much for your answer. I didn't think like that before. See you at other question.

Raju Pratama - 2 years, 5 months ago

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Please mention the source of this problem. @Raju Pratama

Swapnil Das - 2 years, 5 months ago

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it is my homework from my math course.

Raju Pratama - 2 years, 5 months ago

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O! See my inductive process!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das but I don't get the complete process from you

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama Just put my values of a, b and c in your expression, this is called induction!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das how can you get the value of a, b, and c?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama By random thinking bro! You may take other's too! like 4, 1/4 and 1!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das what induction is?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama See Wikipedia on Mathematical Induction. The explanation given by Swapnil is incorrect.

Karthik Venkata - 2 years, 5 months ago

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@Raju Pratama Well, it's kinda technique used to prove mathematical theorems by taking random values, rather than actually proving them by expressions and hard simplifications!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das This is the worst misconception of Mathematical Induction :/ !

Karthik Venkata - 2 years, 5 months ago

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@Karthik Venkata Hey, I saw my mistypes! Actually I meant Inductive reasoning! Sorry for that!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das Ya, No problem. but by the way what the different between Inductive reasoning and Mathematical Induction?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama Well,... I donno how should I explain, BTW angry on my math teacher, It was he who misconceptualized my brain!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das Oooh, I'm sorry to hear that.

Raju Pratama - 2 years, 5 months ago

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@Karthik Venkata O, I really don't know about it before. Thank's a lot ffor your explaination Karthik Venkata

Raju Pratama - 2 years, 5 months ago

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@Swapnil Das but, do you have a manual way? because my teacher asked me to write the process.

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama Ya, but difficult to edit!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das if I express 4, 1/4, and 1. I don't get the answer. how about other values?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama U don't ! Lemme try!

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das how if a = -1, b = -1, and c = 1 ?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama YA!

Swapnil Das - 2 years, 5 months ago

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If U give me sufficient time, I can provide you the complete process by trying myself.

Swapnil Das - 2 years, 5 months ago

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Well by what time do you want the answer?

Swapnil Das - 2 years, 5 months ago

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at 20.45

Raju Pratama - 2 years, 5 months ago

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What's time now? ( Your profile suggests that U live in Indonesia)

Swapnil Das - 2 years, 5 months ago

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@Swapnil Das well, maybe you can solve it in 15 minutes

Raju Pratama - 2 years, 5 months ago

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@Swapnil Das 20.30

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama My goodness!

Swapnil Das - 2 years, 5 months ago

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Please replace my induction with inductive reasoning, I was mistakened as my teacher gave me a wrong explanation. Thanks!

Swapnil Das - 2 years, 5 months ago

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Did U get it?

Swapnil Das - 2 years, 5 months ago

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no, I don't, but would you like to explain the complete process to me?

Raju Pratama - 2 years, 5 months ago

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Think of some numbers a,b,c such that abc=1, I thought and found out! Then put them in the expression!

Swapnil Das - 2 years, 5 months ago

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@Raju Pratama It's one! I did it by induction! take a =2, b=1/2 and c = 1 !

Swapnil Das - 2 years, 5 months ago

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Lol how can it be called induction Swapnil Das ? I think you are confused between Inductive reasoning (guessing) and Mathematical Induction ! See this.

Karthik Venkata - 2 years, 5 months ago

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please comment.

Raju Pratama - 2 years, 5 months ago

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I think the answer is one.

Swapnil Das - 2 years, 5 months ago

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how the way?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama I have not tried, just U try to take the following method I always use, abc=1, then a=??, and go on!

Swapnil Das - 2 years, 5 months ago

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What's your age bro?

Swapnil Das - 2 years, 5 months ago

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17 years old, how about you?

Raju Pratama - 2 years, 5 months ago

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@Raju Pratama O! I am 14 sir!!

Swapnil Das - 2 years, 5 months ago

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