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#1 2019-03-12 15:00:00

mrpace
Member
Registered: 2012-08-16
Posts: 79

Please help me with a proof

Find all pairs of real numbers (a,b) such that a/b + b/a >= 2

Any help appreciated

Thanks

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#2 2019-03-13 01:35:06

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,462

Re: Please help me with a proof

hi mrpace

Depends on the sign of a and b.

if

If a and b have same sign (both positive or both negative)

This will be true for all a and b ∈ {reals}

If a and b have opposite signs the inequality switches:

I'll leave you to finish this off.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy smile

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#3 2019-03-16 00:43:42

Alg Num Theory
Member
Registered: 2017-11-24
Posts: 342
Website

Re: Please help me with a proof

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