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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 725

In my maths test there came this question:

a+b+c=10

a²+b²+c²=38

a³+b³+c³=160

Find the values of a,b and c.

Please tell me the answer with explanation.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I got this far:

Here are the divisors of 280

{1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280}

It is easy to finish now.

Welcome to the forum.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 725

Hi, thickhead yours is the right solution. Thanks for helping me

But thickhead I couldn't get how did you simplified from equation (2) to equation(4) i.e.

ab=30/c and a+b=10-c

so c³-10c²+31c-30=0

In (2) first term ab is clear ;second and third terms have c common i.e.c(a+b)=c(10-c). i hope you can simplify further.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

In (2) first term ab is clear ;second and third terms have c common i.e.c(a+b)=c(10-c). i hope you can simplify further.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

Hi **iamaditya**,(really it is false;it is you who is aditya)

Suppose only first and second equations are given with a,b,c as positive integers. Can you evolve a method to find the numbers? Not purely hit and try method (Ram bharosa method) but with some logic in it.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 725

If only the first 2 equations i.e. a+b+c=10 and a²+b²+c²=38 are given then it is impossible to work out as there are three unknown variables and only 2 equations.

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

But then there is the condition that they are only natural numbers.That limits the scope of the solution and gives only one solution.

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 860

iamaditya wrote:

If only the first 2 equations i.e. a+b+c=10 and a²+b²+c²=38 are given then it is impossible to work out as there are three unknown variables and only 2 equations.

By trial and error, I find the solutions are 2, 3, and 5, though I don't know how to do it algebraically.

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**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

Trial and error no dobt,but systematically. e.g. if you assume a<b<c since there is nothing to choose among them, c has very limited value.To start with c<=6. once c=6 fails you come to c=5.

(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha

{Gods rejoice at those places where ladies are respected.}

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 725

Yeah thickhead you are right.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

By trial and error, I find the solutions are 2, 3, and 5, though I don't know how to do it algebraically.

That guy in post #2 whittles down the possibilities.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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