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Question Number 55193 by naka3546 last updated on 19/Feb/19

Answered by Meritguide1234 last updated on 20/Feb/19

by cauchy triangle inequality  x≥(√2)(a−b+1+...+c−a+1)  min x=3(√2) ,a=b=c=(1/2)  x^2 −3x+7=25−9(√2)

$$\mathrm{by}\:\mathrm{cauchy}\:\mathrm{triangle}\:\mathrm{inequality} \\ $$$$\mathrm{x}\geqslant\sqrt{\mathrm{2}}\left(\mathrm{a}−\mathrm{b}+\mathrm{1}+...+\mathrm{c}−\mathrm{a}+\mathrm{1}\right) \\ $$$$\mathrm{min}\:\mathrm{x}=\mathrm{3}\sqrt{\mathrm{2}}\:,\mathrm{a}=\mathrm{b}=\mathrm{c}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{7}=\mathrm{25}−\mathrm{9}\sqrt{\mathrm{2}} \\ $$

Commented by naka3546 last updated on 19/Feb/19

how  to  get  it ?  are  you  sure?

$${how}\:\:{to}\:\:{get}\:\:{it}\:?\:\:{are}\:\:{you}\:\:{sure}? \\ $$

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