Math Is Fun Forum

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

A simple question is not being able to solve by me

Last edited by iamaditya (2017-10-04 18:30:28)

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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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A simple question is not being able to solve by me

I'm wondering what happens if you just expand the brackets.  Bit buzy right now.  I'll have a look later.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: A simple question is not being able to solve by me

I'm sorry I gave the question wrong, I edited it . Now see.

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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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A simple question is not being able to solve by me

And is that xyz = 1 rather than abc = 1  ?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A simple question is not being able to solve by me

I've assumed that it's xyz = 1

Then I put everything over a common denominator, expanded all brackets and simplified.  The numerator and denominator came out the same so the expression = 1

It was a very complicated expansion, taking two sheets of A4, even with simplifications such as x.y^2.z = y so I won't post it here just yet.  I'll look for an easier way first.  Phew!

later edit: got it down to half a page of working but still the same method.

Bob

Last edited by Bob (2017-10-04 01:00:17)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

iamaditya

Member

From: Planet Mars

Registered: 2016-11-15

Posts: 821

Re: A simple question is not being able to solve by me

And is that xyz = 1 rather than abc = 1  ?

Bob

Yeah it is.

I solved it but it took 2 whole pages to solve it. Phew! I finally got the numerator and denominator as equal and hence it is equal to 1.

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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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A simple question is not being able to solve by me

Yes, me too.

I managed to shorten the proof by re-writing like this

and so on.

I feel as though there ought to be a 'slick' way to do this easily, but I haven't found it yet.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: A simple question is not being able to solve by me

I think you're going to love this:

multiply the first term top and bottom by y and the third by xy:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob