First Proofs class.

• Jan 13th 2012, 03:08 PM
resjsu
First Proofs class.
So the semester just started and im already drowning. Im usually pretty good at math but I just dont get proofs.

I need help with a few problems (ive already attempted them multiple times), ill just post one at a time.

The first one:
from 'Mathematical Thinking Problem Solving and Proofs 2nd ed.'
1.29
Let x,y,z be nonnegative real numbers such that y+z > or = to 2.
Prove: (x+y+z)^2 is > or = 4x + 4yz

My attempt
I expanded the square and canceled out what I could.

Than I attempted different things from moving the right side over to the left and seeing if I could simply, or grouping the left and seeing if they broke down into smaller elements..

This is not graded homework just practice but the quizzes are very similar to the HW im told so I need to understand this.

• Jan 13th 2012, 03:25 PM
Plato
Re: First Proofs class - HELP!
Quote:

Originally Posted by resjsu
Let x,y,z be nonnegative real numbers such that y+z > or = to 2.
Prove: (x+y+z)^2 is > or = 4x + 4yz

To do this you must know this:
$\left( {\forall a\;\& \;b} \right)\left[ {a^2 + b^2 \ge 2ab} \right]$.

\begin{align*}(x+y+z)^2&=x^2+y^2+z^2+2xy+2xz+2yz\\ &\ge x^2+2x(y+z)+4yz \end{align*}
• Jan 13th 2012, 06:17 PM
resjsu
Re: First Proofs class - HELP!
Hello,

Can you explain how you got the right side?

Where did the x^2 and the 2x(y+z) come from?

I understand that if y+z equals at least 2 then the term turns into the original 4x but how did you know to look at that. Thats the trouble im having I don't know where to look for clues. I would've never thought of that.
• Jan 14th 2012, 07:52 PM
resjsu
Re: First Proofs class - HELP!
• Jan 14th 2012, 08:18 PM
Plato
Re: First Proofs class - HELP!
Quote:

Originally Posted by resjsu
Can YOU expand $(x+y+z)^2~?$