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Category: Algebra

Question-175430

Question Number 175430 by mathlove last updated on 30/Aug/22 Commented by infinityaction last updated on 30/Aug/22 $$\frac{{x}}{{y}+{z}}+\mathrm{1}+\frac{{y}}{{z}+{x}}+\mathrm{1}+\frac{{z}}{{x}+{y}}+\mathrm{1}\:=\mathrm{37} \\ $$$${x}+{y}+{z}\left[\frac{\mathrm{1}}{{y}+{z}}+\frac{\mathrm{1}}{{z}+{x}}+\frac{\mathrm{1}}{{x}+{y}}\right]\:=\:\mathrm{37} \\ $$$$\frac{\mathrm{1}}{{y}+{z}}+\frac{\mathrm{1}}{{z}+{x}}+\frac{\mathrm{1}}{{x}+{y}}\:=\:\frac{\mathrm{37}}{\mathrm{2022}} \\ $$ Commented by…

7-67-667-6667-n-terms-

Question Number 175411 by Rasheed.Sindhi last updated on 29/Aug/22 $$ \\ $$$$\mathrm{7}+\mathrm{67}+\mathrm{667}+\mathrm{6667}+…..\left({n}\:{terms}\right)=? \\ $$$$ \\ $$ Commented by infinityaction last updated on 30/Aug/22 $$\left(\mathrm{6}+\mathrm{1}\right)+\left(\mathrm{66}+\mathrm{1}\right)+\left(\mathrm{666}+\mathrm{1}\right)+…\left({n}\:{terms}\right) \\…

Question-175396

Question Number 175396 by Shrinava last updated on 29/Aug/22 Answered by mahdipoor last updated on 29/Aug/22 $${x}+{y}^{\mathrm{2}} \sqrt{\frac{\mathrm{2}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }}\geqslant{y}+\sqrt{\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\mathrm{2}}}\:\:\:\Leftrightarrow \\ $$$$\left({x}+{y}^{\mathrm{2}} \sqrt{\frac{\mathrm{2}}{{x}^{\mathrm{2}}…