Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 777

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

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,398

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

Bob

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

Offline

**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 777

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

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,398

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

Bob

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,398

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 bundy (2017-10-04 01:00:17)*

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

Offline

**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 777

bob bundy wrote:

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.

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,398

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,398

I think you're going to love this:

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

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline