Menu Close

Category: Algebra

Be-calm-then-solve-x-2-7x-8-x-3-2-

Question Number 178612 by Acem last updated on 19/Oct/22 $${Be}\:{calm}\:{then}\:{solve}\:\mid\frac{{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{8}}{{x}+\mathrm{3}}\mid\geqslant\:\mathrm{2} \\ $$ Answered by cortano1 last updated on 19/Oct/22 $$\:\mathrm{x}\neq−\mathrm{3} \\ $$$$\:\mid\mathrm{x}^{\mathrm{2}} +\mathrm{7x}−\mathrm{8}\mid\geqslant\mid\mathrm{2x}+\mathrm{6}\mid \\…

Let-a-b-2023-Find-values-of-a-b-N-

Question Number 178596 by Acem last updated on 18/Oct/22 $${Let}\:\sqrt{{a}}+\:\sqrt{{b}}=\:\sqrt{\mathrm{2023}}\:\:\:,\:{Find}\:{values}\:{of}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$ Commented by mr W last updated on 18/Oct/22 $${a}=\mathrm{7}\left(\mathrm{17}−{n}\right)^{\mathrm{2}} \\ $$$${b}=\mathrm{7}{n}^{\mathrm{2}} \\ $$$${with}\:{n}=\mathrm{1},\mathrm{2},…,\mathrm{16}…

Solve-2x-x-1-3-

Question Number 178595 by Acem last updated on 18/Oct/22 $${Solve}\:\frac{\mathrm{2}{x}}{{x}+\mathrm{1}}\geqslant\:\mathrm{3} \\ $$ Answered by Acem last updated on 19/Oct/22 $${The}\:{safest}\:{and}\:{surest}\:{way}\:{to}\:{avoid}\:{making} \\ $$$$\:{mental}\:{mistakes}: \\ $$$$ \\…

prove-that-a-cosh-1-x-ln-x-x-2-1-b-tanh-1-x-1-2-ln-x-1-x-1-x-lt-1-

Question Number 178577 by Spillover last updated on 18/Oct/22 $$\mathrm{prove}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\mathrm{cosh}\:^{−\mathrm{1}} \mathrm{x}=\pm\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right) \\ $$$$\left(\mathrm{b}\right)\mathrm{tanh}\:^{−\mathrm{1}} \mathrm{x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right),\mid\mathrm{x}\mid<\mathrm{1} \\ $$ Answered by depressiveshrek last updated on…