The minimum value of polynomials.

Algebra Level 2

Given non-negative real numbers $a, b$ and $c$ satisfying $ab+bc+ca=3$ and $a \ge c$ .

Find the minimum value of $P=\frac{1}{(a+1)^{2}} + \frac{2}{(b+1)^{2}} + \frac{3}{(c+1)^{2}}$ ?

Bonus: In order to get the minimum value of $P$ , what value should $a, b, c$ be?

Clarification: Type your answer as the minimum value of $P$ .

The answer is 3.

1 solution

A Former Brilliant Member
Apr 25, 2019

For a=b=c=1, the condition ab+bc+ca=3 is met. Then the value of P is 1.5 which is less than 3. Where am I going wrong? a>=c implies a>=√((b^2)+3)-b. For b=1 a>=1. Why should the option a=b=c=1 not be valid?

I also tried 1.5 but only integers are allowed. Then I did 0 and 1 incorrect. Then randomly wrote 3 and got correct.

Mr. India - 2 years, 1 month ago

Let's put this as a report

A Former Brilliant Member - 2 years, 1 month ago

The minimum value of polynomials.

The answer is 3.

1 solution

2 pending reports

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