Category: Algebra

Question Number 196299 by hardmath last updated on 22/Aug/23 $$\mathrm{If}\:\rightarrow\:\mathrm{y}\:=\:\mathrm{x}\:!\:\:\:\:\:\mathrm{find}\:\rightarrow\:\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$ Answered by Frix last updated on 22/Aug/23 $${y}={x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{derivative} \\ $$$$\mathrm{exists}. \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{mean}\:{x}!=\Gamma\:\left({x}+\mathrm{1}\right): \\…

Question Number 196288 by mathlove last updated on 22/Aug/23 $$\mathrm{4}^{{x}} =\sqrt{\mathrm{5}^{{y}} }=\mathrm{400} \\ $$$$\frac{{xy}}{\mathrm{2}{x}+{y}}=? \\ $$ Commented by hardmath last updated on 22/Aug/23 $$\rightarrow\:\mathrm{x}\:=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{20}\right)…

Question Number 196185 by cortano12 last updated on 19/Aug/23 $$\:\:\:\underbrace{\:} \\ $$ Commented by AST last updated on 19/Aug/23 $${When}\:{x}={y}={z}\:\wedge\:{a}={b}={c};\frac{{ab}+{bc}+{ca}}{{bc}}=\mathrm{3} \\ $$$${When}\:{x}=−\mathrm{1},{y}=\mathrm{1},{z}=\mathrm{1};\:\frac{{ab}+{bc}+{ca}}{{bc}}=\frac{{a}\left({b}+{c}\right)}{{bc}}+\mathrm{1} \\ $$$${can}\:{get}\:{multiple}\:{values}\:{since}\:{a},{b},{c}\:{can}\:{vary}. \\…

Question Number 196165 by mathlove last updated on 19/Aug/23 $$\left.\begin{matrix}{{x}^{{x}+{y}} ={y}^{\mathrm{24}} }\\{{y}^{{x}+{y}} ={x}^{\mathrm{6}} }\end{matrix}\right\}\Rightarrow\left({x},{y}\right)=\left(?,?\right) \\ $$ Answered by liuxinnan last updated on 19/Aug/23 Answered by…

Question Number 196119 by mr W last updated on 18/Aug/23 $${solve} \\ $$$$\sqrt{\mathrm{100}−{x}^{\mathrm{2}} }+\sqrt{\mathrm{64}−{x}^{\mathrm{2}} }=\mathrm{12} \\ $$ Answered by cortano12 last updated on 18/Aug/23 $$\:\sqrt{\left(\mathrm{10}−\mathrm{x}\right)\left(\mathrm{10}+\mathrm{x}\right)}\:+\sqrt{\left(\mathrm{8}−\mathrm{x}\right)\left(\mathrm{8}+\mathrm{x}\right)}\:=\:\mathrm{12}…