Category: Algebra

Question Number 131697 by mathlove last updated on 07/Feb/21 $$x^x=6x=?$$ Answered by mr W last updated on 07/Feb/21 $$x=6^{\frac{1}{x}}=e^{\frac{\ln 6}{x}}$$$$\frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{6}}{{x}}}…

Question Number 131688 by liberty last updated on 07/Feb/21 $$\mathrm{Let}\alpha \mathrm{and}\beta \mathrm{are}\mathrm{the}\mathrm{roots}$$$$\mathrm{of}\mathrm{the}\mathrm{equation}{\mathrm{x}}^2-6\mathrm{x}-2=0.$$$$\mathrm{If}{a}_n={\alpha }^n-{\beta }^n\mathrm{for}n⩾1$$$$\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{a_{10}-2a_8}{2a_9}?$$…

Question Number 588 by shaleen last updated on 03/Feb/15 $$(a+b=10)(a+c=24)(b+c=20)$$$$findabc$$ Answered by prakash jain last updated on 03/Feb/15 $$a+b=10\Rightarrow b=10-a$$$${a}+{c}=\mathrm{24}\Rightarrow{c}=\mathrm{24}−{a}…

Question Number 131640 by Salman_Abir last updated on 07/Feb/21 Answered by EDWIN88 last updated on 07/Feb/21 $$$$$$\mathrm{Du}\mathrm{bist}\mathrm{wundersch}\ddot{\mathrm{o}n}$$ Commented by EDWIN88…

Question Number 482 by prakash jain last updated on 12/Jan/15 $$\mathrm{The}\mathrm{number}1000!\mathrm{has}\mathrm{certain}\mathrm{number}$$$$\mathrm{of}0s\mathrm{at}\mathrm{the}\mathrm{end},\mathrm{what}\mathrm{the}\mathrm{the}\mathrm{first}\mathrm{non}-\mathrm{zero}$$$$\mathrm{digit}.$$$$1000!=\dots {\mathrm{d}}_1{\mathrm{d}}_2{\mathrm{d}}_3\mathrm{D}00000\dots$$$$\mathrm{where}\:\mathrm{d}_{\mathrm{1}} ,\mathrm{d}_{\mathrm{2}} ,\mathrm{d}_{\mathrm{3}} ,\mathrm{D}\:\mathrm{are}\:\mathrm{digits}.…