# proof question with Cauchy-Schwarz inequality

#### hearts123

##### New member
hi everyone! Here's a proof question that I'm having trouble with.
I know what the Cauchy-Schwarz inequality is, but I don't know how to apply it.
My teacher mentioned that we should try "constructing" or changing the numbers so that the C-S inequality can be applied.

a and b are both real numbers, a+b = 1
using the Cauchy-Schwarz inequality, prove that 1/a + 1/b >=4

Any help is greatly appreciated! #### pka

##### Elite Member
hi everyone! Here's a proof question that I'm having trouble with.
I know what the Cauchy-Schwarz inequality is, but I don't know how to apply it.
My teacher mentioned that we should try "constructing" or changing the numbers so that the C-S inequality can be applied.
a and b are both real numbers, a+b = 1. using the Cauchy-Schwarz inequality, prove that 1/a + 1/b >=4
You posted "I know what the Cauchy-Schwarz inequality" why do't you tell us what for you know.
For most mathematicians the C-S is operative in an inner product space. That does not work here.
Here is one very very simple form: $$\displaystyle a^2+b^2\ge 2ab$$.
So post what you know.

• hearts123

#### hearts123

##### New member
You posted "I know what the Cauchy-Schwarz inequality" why do't you tell us what for you know.
For most mathematicians the C-S is operative in an inner product space. That does not work here.
Here is one very very simple form: $$\displaystyle a^2+b^2\ge 2ab$$.
So post what you know.
I have an appointment in a few minutes, but I'll post what I know about the C-S inequality asap. Thanks!