Category: Algebra

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}…

Question Number 196056 by mr W last updated on 17/Aug/23 $${solve} \\ $$$$\sqrt{\mathrm{2}{x}+\mathrm{3}}−\sqrt{\mathrm{3}{x}+\mathrm{8}}=\sqrt{\mathrm{3}{x}+\mathrm{4}}−\sqrt{\mathrm{2}{x}+\mathrm{7}} \\ $$ Answered by cortano12 last updated on 17/Aug/23 $$\:\sqrt{\mathrm{u}}\:−\sqrt{\mathrm{v}+\mathrm{4}}\:=\sqrt{\mathrm{v}}−\sqrt{\mathrm{u}+\mathrm{4}} \\ $$$$\:\:\sqrt{\mathrm{u}}−\sqrt{\mathrm{v}}\:=\:\sqrt{\mathrm{v}+\mathrm{4}}−\sqrt{\mathrm{u}+\mathrm{4}}…