Category: Algebra

Question Number 58084 by Tawa1 last updated on 17/Apr/19 Commented by MJS last updated on 17/Apr/19 $$\mathrm{sorry}\mathrm{but}\mathrm{do}\mathrm{you}\mathrm{really}\mathrm{believe}\mathrm{someone}$$$$\mathrm{on}\mathrm{this}\mathrm{forum}\mathrm{could}\mathrm{be}\mathrm{able}\mathrm{to}\mathrm{solve}\mathrm{problems}$$$$\mathrm{which}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{be}\mathrm{solved}\mathrm{by}\mathrm{the}\mathrm{greatest}$$$$\mathrm{mathematicians}\mathrm{of}\mathrm{our}\mathrm{time}?$$…

Question Number 189137 by Shrinava last updated on 12/Mar/23 $$\mathrm{It}\mathrm{is}\mathrm{known}\mathrm{that}\mathrm{x}\mathrm{is}\mathrm{rational}$$$$\mathrm{x}\sqrt{28+3\sqrt{28+3\sqrt{28+3\sqrt{?}}}}$$$$\mathrm{Find}\mathrm{the}\mathrm{dufference}\mathrm{of}\mathrm{possible}\mathrm{vaules}$$$$\mathrm{of}\mathbf{x}$$ Commented by mr W last updated on…

Question Number 189132 by Shrinava last updated on 12/Mar/23 $$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}$$$$\mathrm{in}\mathrm{the}\mathrm{system}\mathrm{of}\mathrm{equations}:$$$$\{\begin{array}{l}13\mathrm{a}+2\mathrm{b}+\mathrm{c}+6\mathrm{d}+2\mathrm{e}=96\\ 5\mathrm{a}+9\mathrm{b}+2\mathrm{c}+7\mathrm{d}+3\mathrm{e}=75\\ 7\mathrm{a}+8\mathrm{b}+17\mathrm{c}+11\mathrm{d}+7\mathrm{e}=99\\ 3\mathrm{a}+3\mathrm{b}+3\mathrm{c}+\mathrm{d}+8\mathrm{e}=55\\ \mathrm{a}+7\mathrm{b}+6\mathrm{c}+4\mathrm{d}+9\mathrm{e}=79\end{array}$$ Answered by mr W last updated on 12/Mar/23 $${say}\:{f}={a}+{b}+{c}+{d}+{e}…

Question Number 189131 by Shrinava last updated on 12/Mar/23 Answered by cortano12 last updated on 12/Mar/23 $$\sqrt{19+2\sqrt{4\times 15}}=2+\sqrt{15}$$ Answered by BaliramKumar last updated on…

Question Number 189124 by Rupesh123 last updated on 12/Mar/23 Answered by witcher3 last updated on 15/Mar/23 $$\mathrm{x}+\mathrm{y}+\mathrm{x}⩾3\sqrt[3]{\mathrm{xyz}}$$$$\iff \mathrm{xyz}⩾3\sqrt[3]{\mathrm{xyz}};\mathrm{let}\mathrm{a}=\mathrm{xyz}$$$$\iff \mathrm{a}⩾3\sqrt[3]{\mathrm{a}}\Rightarrow {\mathrm{a}}^{\frac{2}{3}}⩾3\Rightarrow \mathrm{a}⩾\sqrt[2]{27}=3\sqrt{3}$$$$\mathrm{a}+\frac{\mathrm{1}}{\mathrm{a}}=\mathrm{f}\left(\mathrm{a}\right)\geqslant\mathrm{2},\forall\mathrm{a}>\mathrm{0} \…