Proving an expression (1 Viewer)

planino · Apr 29, 2012

Given p>0, prove p +¹/_p >= 2

I hate of these proving questions (but the process of solving them is quite fun, I just hate them cos I can't get them right

)

planino · Apr 29, 2012

nightweaver066 · Apr 29, 2012

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

$p^2 + 1 \geq 2p$

$p^2 - 2p + 1 \geq 0$

$(p -1)^2 \geq 0$

$$Sketch $ y = (p -1)^2$

$For~p > 0,~ clearly~ (p - 1)^2 \geq 0$

Or you could prove by induction from the second line.

Or you could sketch the $p + \frac{1}{p}$ and show for p > 0, it's greater than or equal to 2.

bleakarcher · Apr 29, 2012

planino said:
Given p>0, prove p +¹/_p >= 2

I hate of these proving questions (but the process of solving them is quite fun, I just hate them cos I can't get them right )

A tip for the future, with these questions (inequalities) you have a set of known statements and then from those you can derive the more non-obvious ones.

[sqrt(p)-(1/sqrt(p))]^2>=0 where p>0 (p real) since the square of any real is always positive
p+(1/p)-2>=0
p+(1/p)>=2

planino · Apr 30, 2012

Thanks guys!

Proving an expression (1 Viewer)

planino

Member

planino

Member

nightweaver066

Well-Known Member

bleakarcher

Active Member

planino

Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)