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Question-191706




Question Number 191706 by BaliramKumar last updated on 29/Apr/23
Answered by Skabetix last updated on 29/Apr/23
→(b) ((97)/(36))
$$\rightarrow\left({b}\right)\:\frac{\mathrm{97}}{\mathrm{36}} \\ $$
Answered by Skabetix last updated on 29/Apr/23
2x+((9/x))=9  2x^2 +9=9x  2x^2 −9x+9=0  x_1 =(3/2) and x_2 =3  → 3^2 +(1/3^2 )=((82)/9)  →((3/2))^2 +((1/(((3/2))^2 )))=((97)/(36))  obviously ((97)/(36))<((82)/9)  →answer b
$$\mathrm{2}{x}+\left(\frac{\mathrm{9}}{{x}}\right)=\mathrm{9} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{9}=\mathrm{9}{x} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{9}=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =\frac{\mathrm{3}}{\mathrm{2}}\:{and}\:{x}_{\mathrm{2}} =\mathrm{3} \\ $$$$\rightarrow\:\mathrm{3}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }=\frac{\mathrm{82}}{\mathrm{9}} \\ $$$$\rightarrow\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} }\right)=\frac{\mathrm{97}}{\mathrm{36}} \\ $$$$\boldsymbol{\mathrm{obviously}}\:\frac{\mathrm{97}}{\mathrm{36}}<\frac{\mathrm{82}}{\mathrm{9}} \\ $$$$\rightarrow{answer}\:\mathrm{b} \\ $$
Commented by BaliramKumar last updated on 29/Apr/23
Thanks
$$\mathrm{Thanks} \\ $$

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