Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

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

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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

Alg Num Theory

Member

Registered: 2017-11-24

Posts: 693

Website

Re: Please help me with a proof

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Me, or the ugly man, whatever (3,3,6)