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Question Number 126175 by naka3546 last updated on 17/Dec/20

$$Provethat$$$$a^2+b^2+c^2+6⩾3(a+b+c)$$$$a,b,c\in {\mathbb{R}}^{+}$$

Commented by PRITHWISH SEN 2 last updated on 18/Dec/20

$${(\mathrm{a}-2)}^2⩾-(\mathrm{a}-2)\mathrm{equality}\mathrm{holds}\mathrm{for}\mathrm{a}=1$$$$\Rightarrow {\mathrm{a}}^2+2⩾3\mathrm{a}$$$$\mathrm{similariy}$$$${\mathrm{b}}^2+2⩾3\mathrm{b}$$$${\mathrm{c}}^2+2⩾3\mathrm{c}$$$$\mathrm{adding}$$$${\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2+6⩾3(\mathrm{a}+\mathrm{b}+\mathrm{c})$$

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