Proving inequalities using binomial expansion

If x and y are real nos. not equal to zero, show that

\frac{x^2}{y^2}+\frac{16y^2}{x^2}+24\geq\frac{8x}{ y}+\frac{32y}{x}.

The book hinted that binomial thingy (maybe expansion, I forgot) may be used.

EDIT:

BTW, please teach me how to use that \frac, \leq, etc.

Re: Proving inequalities using binomial expansion

Quote:

Originally Posted by

**Kaloda** If x and y are real nos. not equal to zero, show that

\frac{x^2}{y^2}+\frac{16y^2}{x^2}+24\geq\frac{8x}{ y}+\frac{32y}{x}.

The book hinted that binomial thingy (maybe expansion, I forgot) may be used.

EDIT:

BTW, please teach me how to use that \frac, \leq, etc.

Your code looks alright, but you need to put it inside tex tags.

Re: Proving inequalities using binomial expansion

Quote:

Originally Posted by

**Kaloda** If x and y are real nos. not equal to zero, show that

The book hinted that binomial thingy (maybe expansion, I forgot) may be used.

EDIT:

BTW, please teach me how to use that \frac, \leq, etc.

Try multiplying both sides of the inequality by (this is positive, so you haven't changed the inequality).

Then rearrange all the terms on one side of the inequality (so you have ) and see if you can apply the thingy.

Re: Proving inequalities using binomial expansion

Ah. Thank you for the proper syntax.

So this is the question

The book farther hinted that you may let then use the binomial expansion

And BTW, if you know another solution, please post it even though it doesn't follow the book's solution.

Re: Proving inequalities using binomial expansion

Well following the book's example we have

which is a true statement and therefore confirms the original statement.

Re: Proving inequalities using binomial expansion

I already proved it by multiplying as what awkward said. But thanks Prove it for that brilliant solution.