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Question Number 75883 by TawaTawa last updated on 19/Dec/19

$$\mathrm{If}{\mathrm{a}}^4+{\mathrm{b}}^4+{\mathrm{c}}^4+{\mathrm{d}}^4=16$$$$\mathrm{Prove}\mathrm{that},{\mathrm{a}}^5+{\mathrm{b}}^5+{\mathrm{c}}^5+{\mathrm{d}}^5⩽32$$

Commented by prakash jain last updated on 19/Dec/19

$$a^4⩽16$$$$\Rightarrow -2⩽a⩽2$$$$a,b,c,d\mathrm{all}\mathrm{lie}\mathrm{in}\mathrm{range}[-2,2]$$$$\Rightarrow a^5+b^5+c^5+d^5$$$$⩽2(a^4+b^4+c^4+d^4)=32◼$$

Commented by TawaTawa last updated on 23/Dec/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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