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# Find abc !

Note by Raju Pratama
2 years, 2 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. · 2 years, 2 months ago

thank's very much for your answer. I didn't think like that before. See you at other question. · 2 years, 2 months ago

Please mention the source of this problem. @Raju Pratama · 2 years, 2 months ago

it is my homework from my math course. · 2 years, 2 months ago

O! See my inductive process! · 2 years, 2 months ago

but I don't get the complete process from you · 2 years, 2 months ago

Just put my values of a, b and c in your expression, this is called induction! · 2 years, 2 months ago

how can you get the value of a, b, and c? · 2 years, 2 months ago

By random thinking bro! You may take other's too! like 4, 1/4 and 1! · 2 years, 2 months ago

what induction is? · 2 years, 2 months ago

See Wikipedia on Mathematical Induction. The explanation given by Swapnil is incorrect. · 2 years, 2 months ago

Well, it's kinda technique used to prove mathematical theorems by taking random values, rather than actually proving them by expressions and hard simplifications! · 2 years, 2 months ago

This is the worst misconception of Mathematical Induction :/ ! · 2 years, 2 months ago

Hey, I saw my mistypes! Actually I meant Inductive reasoning! Sorry for that! · 2 years, 2 months ago

Ya, No problem. but by the way what the different between Inductive reasoning and Mathematical Induction? · 2 years, 2 months ago

Well,... I donno how should I explain, BTW angry on my math teacher, It was he who misconceptualized my brain! · 2 years, 2 months ago

Oooh, I'm sorry to hear that. · 2 years, 2 months ago

O, I really don't know about it before. Thank's a lot ffor your explaination Karthik Venkata · 2 years, 2 months ago

but, do you have a manual way? because my teacher asked me to write the process. · 2 years, 2 months ago

Ya, but difficult to edit! · 2 years, 2 months ago

if I express 4, 1/4, and 1. I don't get the answer. how about other values? · 2 years, 2 months ago

U don't ! Lemme try! · 2 years, 2 months ago

how if a = -1, b = -1, and c = 1 ? · 2 years, 2 months ago

YA! · 2 years, 2 months ago

If U give me sufficient time, I can provide you the complete process by trying myself. · 2 years, 2 months ago

Well by what time do you want the answer? · 2 years, 2 months ago

at 20.45 · 2 years, 2 months ago

What's time now? ( Your profile suggests that U live in Indonesia) · 2 years, 2 months ago

well, maybe you can solve it in 15 minutes · 2 years, 2 months ago

20.30 · 2 years, 2 months ago

My goodness! · 2 years, 2 months ago

Please replace my induction with inductive reasoning, I was mistakened as my teacher gave me a wrong explanation. Thanks! · 2 years, 2 months ago

Did U get it? · 2 years, 2 months ago

no, I don't, but would you like to explain the complete process to me? · 2 years, 2 months ago

Think of some numbers a,b,c such that abc=1, I thought and found out! Then put them in the expression! · 2 years, 2 months ago

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

Lol how can it be called induction Swapnil Das ? I think you are confused between Inductive reasoning (guessing) and Mathematical Induction ! See this. · 2 years, 2 months ago

please comment. · 2 years, 2 months ago

I think the answer is one. · 2 years, 2 months ago

how the way? · 2 years, 2 months ago

I have not tried, just U try to take the following method I always use, abc=1, then a=??, and go on! · 2 years, 2 months ago

What's your age bro? · 2 years, 2 months ago

17 years old, how about you? · 2 years, 2 months ago