Category: Arithmetic

Question Number 136500 by rexford last updated on 22/Mar/21 Answered by Dwaipayan Shikari last updated on 22/Mar/21 $$a-2d+a-d+a+a+d+a+2d+a+3d=78$$$$\Rightarrow 6a+3d=78\Rightarrow 2a+d=26$$$$sincea-2d>1\Rightarrow a>2d+1Greatestpossiblewhena=2d+1$$$$\mathrm{2}{a}+{d}=\mathrm{26}\Rightarrow\mathrm{5}{d}+\mathrm{2}=\mathrm{26}\Rightarrow\Rightarrow{d}=\frac{\mathrm{24}}{\mathrm{5}} \…

Question Number 70898 by Henri Boucatchou last updated on 09/Oct/19 $$\mathit{S}\mathit{o}\mathit{l}\mathit{v}\mathit{e}:$$$$1.)\sqrt{\mathit{x}-2}+\sqrt{4-\mathit{x}}={\mathit{x}}^2-6\mathit{x}+11$$$$2.){\mathit{x}}^4+{\mathit{x}}^3-2{\mathit{a}\mathit{x}}^2-\mathit{a}\mathit{x}+{\mathit{a}}^2=0$$ Answered by MJS…

Question Number 70780 by MJS last updated on 08/Oct/19 $$\frac{1}{t+\sqrt{u}+\sqrt{v}}=$$$$=\frac{(t-\sqrt{u}+\sqrt{v})(t+\sqrt{u}-\sqrt{v})(t-\sqrt{u}-\sqrt{v})}{(t+\sqrt{u}+\sqrt{v})(t-\sqrt{u}+\sqrt{v})(t+\sqrt{u}-\sqrt{v})(t-\sqrt{u}-\sqrt{v})}=$$$$=\frac{t^3-(\sqrt{u}+\sqrt{v})t^2-{(\sqrt{u}-\sqrt{v})}^{2}t+(u-v)(\sqrt{u}-\sqrt{v})}{t^4-2(u+v)t^2+{(u-v)}^2}$$$$$$$$\frac{\mathrm{1}}{{t}+\sqrt[{\mathrm{3}}]{{u}}+\sqrt[{\mathrm{3}}]{{v}}}= \…

Question Number 70757 by MJS last updated on 08/Oct/19 $$.$$ Commented by TawaTawa last updated on 07/Oct/19 $$\mathrm{Sir},\mathrm{help}\mathrm{me}\mathrm{with}\mathrm{the}\mathrm{question}\mathrm{number}\mathrm{of}\mathrm{a}\mathrm{question}\mathrm{you}\mathrm{solved}$$$$\mathrm{sometimes}.$$$$ \…

Question Number 5081 by FilupSmith last updated on 10/Apr/16 $$\mathrm{Can}\mathrm{we}\mathrm{prove}:$$$$a+a^a+a^{a^a}+\dots =\mathrm{\infty },a>1$$ Answered by Yozzii last updated on 11/Apr/16 $${Define}\:{the}\:{function}\:{f}\:{that}\:{maps}\:…