ONE
    Númas
    ← Back to the programme
    OlympiadMediumInequalities10–12

    If a2+b2+c2=12a^{2} + b^{2} + c^{2} = 12, what is the largest possible value of a+2b+2ca + 2b + 2c?

    Se a2+b2+c2=12a^{2} + b^{2} + c^{2} = 12, qual é o maior valor possível de a+2b+2ca + 2b + 2c?

    Answer options

    Solution

    Step 1 of 3

    1. 1.By Cauchy-Schwarz, (a+2b+2c)2≤(a2+b2+c2)(12+22+22)=12×9(a + 2b + 2c)^{2} \le (a^{2}+b^{2}+c^{2})(1^{2}+2^{2}+2^{2}) = 12 \times 9.