# Algebra problem

#### Vitlu

##### New member
We have that a, b, c>0 and a+b+c=1
What is the minimum value of
a^2+2b^2+c^2?

#### pka

##### Elite Member
We have that a, b, c>0 and a+b+c=1
What is the minimum value of
a^2+2b^2+c^2?
Question: does you notation mean that $$a>0,~b>0,~\&~c>0~?$$

#### JeffM

##### Elite Member
You lose nothing in generality from assuming that $$\displaystyle a \ge b \ge c > 0.$$

I take it that you are not allowed to use calculus?

#### Subhotosh Khan

##### Super Moderator
Staff member
We have that a, b, c>0 and a+b+c=1
What is the minimum value of
a^2+2b^2+c^2?
Please show us what you have tried and exactly where you are stuck.

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