Question Number 142947 by mathdanisur last updated on 07/Jun/21 $${What}\:{is}\:{the}\:{probability}\:{that}\:\mathrm{3}\:{points} \\ $$$${will}\:{fall}\:{twice}\:{when}\:{a}\:{dice}\:{is}\:{thrown} \\ $$$$\mathrm{4}\:{times}? \\ $$ Commented by mr W last updated on 07/Jun/21 $${p}=\frac{{C}_{\mathrm{2}}…
Question Number 142939 by Rasheed.Sindhi last updated on 07/Jun/21 $${Q}#\mathrm{141663}\:{by}\:\:{ajfour}\:{sir}\:{reposted}. \\ $$$$\:\:\:\:\:{x}^{\mathrm{2}} \left({x}−\mathrm{12}\right)\left({x}−\mathrm{15}\right)={k}\left({x}−\mathrm{16}\right)\:;{k}>\mathrm{0} \\ $$$$\:\:\:\:\:{Find}\:{x}\:{in}\:{terms}\:{of}\:{k}. \\ $$ Answered by Rasheed.Sindhi last updated on 07/Jun/21 $$\left\{{x}^{\mathrm{2}}…
Question Number 142936 by Snail last updated on 07/Jun/21 $${Find}\:{all}\:{real}\:{values}\:{of}\:{a}\:\:\:{such}\:{that}\:\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:\: \\ $$$${is}\:{surjective}\:\:{f}\::\boldsymbol{\Re}\Rightarrow\Re \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 142914 by loveineq last updated on 07/Jun/21 $$\mathrm{Let}\:{a}\geqslant{b}\geqslant{c}\geqslant{d}>\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}+{d}\:=\:\mathrm{4}. \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}}{\mathrm{3}}\:\leqslant\:\frac{\mathrm{1}}{\:\sqrt{{d}}} \\ $$$$\mathrm{Prove}\:\mathrm{if}\:\forall{n}\in\mathbb{N}^{+} ,\:\mathrm{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\sqrt[{{n}}]{{a}}+\sqrt[{{n}}]{{b}}+\sqrt[{{n}}]{{c}}}{\mathrm{3}}\:\leqslant\:\frac{\mathrm{1}}{\:\sqrt[{{n}}]{{d}}} \\ $$$$ \\ $$ Terms of…
Question Number 11831 by Peter last updated on 02/Apr/17 $$\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{a}\:−\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\frac{\mathrm{1}}{\mathrm{16}}\:}=\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{16}}} \\ $$$$\mathrm{b}\:−\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}}=\:\sqrt{\mathrm{c}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{25}}} \\ $$$$\mathrm{c}\:−\:\sqrt{\mathrm{b}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}}=\:\sqrt{\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{36}}} \\…
Question Number 142906 by liberty last updated on 07/Jun/21 $${If}\:{abc}=\mathrm{1}\:{and}\:{a},{b},{c}>\mathrm{0}\:{prove} \\ $$$${that}\:\frac{{a}}{{b}^{\mathrm{2}} \left({c}+\mathrm{1}\right)}+\frac{{b}}{{c}^{\mathrm{2}} \left({a}+\mathrm{1}\right)}+\frac{{c}}{{a}^{\mathrm{2}} \left({b}+\mathrm{1}\right)}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by Snail last updated on 07/Jun/21 $${Let}\:{us}\:{recall}\:{Titu}'{s}\:{Lemma}…
Question Number 11813 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17 Commented by mrW1 last updated on 01/Apr/17 $${depending}\:{on}\:{the}\:{values}\:{of}\:{a}\:{and}\:{b}, \\ $$$${there}\:{are}\:\mathrm{5}\:{cases}: \\ $$$$\left.\mathrm{1}\right)\:{no}\:{solution} \\ $$$$\left.\mathrm{2}\right)\:{one}\:{solution} \\ $$$$\left.\mathrm{3}\right)\:{two}\:{solutions}…