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Author: Tinku Tara

if-5-x-y-40-are-in-GP-find-x-and-y-

Question Number 69314 by mezihloic last updated on 22/Sep/19 $${if}\:\mathrm{5}\:{x}\:{y}\:\mathrm{40}\:{are}\:{in}\:{GP}\:.{find}\:{x}\:{and}\:{y} \\ $$ Commented by Rasheed.Sindhi last updated on 22/Sep/19 $$\frac{{x}}{\mathrm{5}}=\frac{{y}}{{x}}=\frac{\mathrm{40}}{{y}} \\ $$$${xy}=\mathrm{200} \\ $$$${x}^{\mathrm{2}} =\mathrm{5}{y}\Rightarrow{x}^{\mathrm{2}}…

Let-a-i-1-i-10-be-the-roots-of-the-equation-m-1-10-mx-m-0-Prove-that-100-i-1-10-a-i-2-1-61-An-algebra-question-as-seen-on-Brilliant-

Question Number 3775 by Yozzii last updated on 20/Dec/15 $${Let}\:{a}_{{i}} \:\left(\mathrm{1}\leqslant{i}\leqslant\mathrm{10}\right)\:{be}\:{the}\:{roots}\:{of}\:{the} \\ $$$${equation}\:\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{mx}^{{m}} =\mathrm{0}.\:{Prove}\:{that} \\ $$$$\mathrm{100}\underset{{i}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}\left({a}_{{i}} ^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{61}. \\ $$$$\left({An}\:{algebra}\:{question}\:{as}\:{seen}\:{on}\:{Brilliant}.\right) \\…