Category: Algebra

Question Number 117082 by bobhans last updated on 09/Oct/20 $$\mathrm{If}6-3\mathrm{x}\mathrm{is}\mathrm{the}\mathrm{geometric}\mathrm{mean}\mathrm{between}$$$$\mathrm{the}\mathrm{integer}{\mathrm{x}}^2+2\mathrm{and}\overline{2}\mathrm{what}\mathrm{are}\mathrm{the}$$$$\mathrm{values}\mathrm{of}\mathrm{x}?$$ Answered by bemath last updated on 09/Oct/20…

Question Number 117026 by bemath last updated on 08/Oct/20 $$\frac{\sqrt{1-\mathrm{x}}}{\sqrt{\mathrm{x}}}+\frac{\sqrt{\mathrm{x}}}{\sqrt{1-\mathrm{x}}}=\frac{13}{6}$$ Answered by 1549442205PVT last updated on 09/Oct/20 $$\mathrm{We}\mathrm{need}\mathrm{the}\mathrm{condition}\mathrm{for}\mathrm{the}\mathrm{equation}$$$$\mathrm{is}\mathrm{defined}\mathrm{as}0<\mathrm{x}<1(\ast )$$$$\:\frac{\sqrt{\mathrm{1}−\mathrm{x}}}{\:\sqrt{\mathrm{x}}}\:+\:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{1}−\mathrm{x}}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}\:\left(\mathrm{1}\right) \…

Question Number 182530 by HeferH last updated on 10/Dec/22 $$If:\frac{a}{x^9}+\frac{x^9}{a}=7$$$$find:\sqrt[4]{\frac{a}{x^9}}+\sqrt[4]{\frac{x^9}{a}}$$ Answered by mr W last updated on…

Question Number 182508 by peter frank last updated on 10/Dec/22 Answered by mahdipoor last updated on 10/Dec/22 $$limf\left(x\right),x\to c=F$$$$\iff \mathrm{\forall }{ϵ}_1>0\mathrm{\exists }{\delta }_1>0\mid x-c\mid <{\delta }_1\Rightarrow \mid F-f\left(x\right)\mid <{ϵ}_1$$$${lim}\:{g}\left({x}\right)\:,\:{x}\rightarrow{c}\:={G}…

Question Number 51431 by Tawa1 last updated on 26/Dec/18 $$\mathrm{Find}\mathrm{x}\mathrm{and}\mathrm{y}$$$${\mathrm{x}}^2+{\mathrm{y}}^2=25\dots \dots \left(\mathrm{i}\right)$$$${\mathrm{x}}^3+{\mathrm{y}}^3=91\dots \dots .\left(\mathrm{ii}\right)$$ Commented by Tawa1 last updated…