Category: Arithmetic

Question Number 127360 by bemath last updated on 29/Dec/20 Answered by liberty last updated on 29/Dec/20 $$let:a-7b,a-6b,a-5b,\dots ,a+5b,a+6b,a+7bisAP$$$$givencondition\to \{\begin{array}{l}3a-18b=-60;a-6b=-20\left(thefirst3terms\right)\\ 3a+18b=84;a+6b=28\left(thelast3terms\right)\end{array}$$$$weget\{\begin{array}{l}a=4\\ b=4\end{array}.wewanttocomputethe$$$${sum}\:{of}\:{the}\:{middle}\:\mathrm{3}\:{terms}\:\Rightarrow{T}_{\mathrm{7}} +{T}_{\mathrm{8}} +{T}_{\mathrm{9}}…

Question Number 61692 by Tony Lin last updated on 06/Jun/19 $$if\frac{3}{2}⩽x⩽5,$$$$prove:2\sqrt{x+1}+\sqrt{2x-3}+\sqrt{15-3x}<2\sqrt{19}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 61479 by Tawa1 last updated on 03/Jun/19 $$\mathrm{Solve}\mathrm{for}\mathrm{x}:\frac{6\sqrt{2\mathrm{x}}}{\mathrm{x}-1}+\frac{5\sqrt{\mathrm{x}-1}}{2\mathrm{x}}=13$$ Commented by MJS last updated on 03/Jun/19 $$\mathrm{we}\mathrm{cannot}\mathrm{generally}\mathrm{solve}\mathrm{this}\dots$$ Answered by ajfour…

Question Number 61313 by Tony Lin last updated on 31/May/19 $$howtocalculate\underset{n\to +\mathrm{\infty }}{\lim 0}.{05}^{0.{05}^{0.{05}^{{.}^{{.}^{.0.05}}}}}\}n$$$$inasimpleandfastway?$$ Commented by mr W…

Question Number 126795 by mathocean1 last updated on 24/Dec/20 $$Nisanumber\in \mathbb{N}whichhasthree$$$$digitsandwrittenxyzinbase10$$$$suchthat\{\begin{array}{l}xy+xz+yz=xyz\\ 0<x<y<z\end{array}$$$$DeterminateN.$$ Commented by JDamian last updated on 24/Dec/20…