Struggling with inequalities. (1 Viewer)

coz707 · Oct 18, 2015

I feel like I was never fully taught how do harder 3u inequalities.

Is there like a set of questions I can complete? Or like some basic proofs I can memorise?

Most questions I just don't know where to start.

Sy123 · Oct 18, 2015

There are some techniques that would let you 'see' the proof to a problem more easily

For instance, you should be familiar with every form of the AM-GM inequality, i.e.

$a^2 + b^2 \geq 2ab$

$(a+b)^2 \geq 4ab$

$a + \frac{1}{a} \geq 2$

$a^3 + b^3 \geq ab(a+b)$

$a^2 + b^2 + c^2 \geq ab + ac + bc$

$\frac{1}{a} + \frac{1}{b} \geq \frac{4}{a+b}$

have a go at proving all of these

Sy123 · Oct 18, 2015

Another tip I can give, is to use all resources of mathematical knowledge at your disposal. For example, using calculus, one can in fact prove:

$a^3+ b^3+c^3 \geq 3abc$

After, all just look at the function

$f(x) = \frac{1}{3} (x^3 + (b^3 + c^3)) - x (3bc) , \ x > 0$

And all you need to do is prove that f(x) >= 0, which can be done like a regular question of this sort using calculus.

Struggling with inequalities. (1 Viewer)

coz707

Member

Sy123

This too shall pass

Sy123

This too shall pass

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