Proving an expression (1 Viewer)

[planino]

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]

bump

 

[nightweaver066]

Or you could prove by induction from the second line.

Or you could sketch the and show for p > 0, it's greater than or equal to 2.

 

[bleakarcher]

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]

Thanks guys!