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Question Number 187905 by Shlock last updated on 23/Feb/23 Commented by Shlock last updated on 23/Feb/23 Let a, b and c be nonnegative real numbers such that a² + b² + c² = 1, prove that Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122360 by benjo_mathlover last updated on 16/Nov/20 Answered by $@y@m last updated on 16/Nov/20 $$\:\:{Put}\:{t}=\left(\sqrt{\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}}\right)^{{x}} \\ $$$$\:\:{t}+\frac{\mathrm{1}}{{t}}=\mathrm{10} \\ $$$${t}^{\mathrm{2}} −\mathrm{10}{t}+\mathrm{1}=\mathrm{0} \\ $$$${t}=\frac{\mathrm{10}\pm\sqrt{\mathrm{100}−\mathrm{4}}}{\mathrm{2}} \\…
Question Number 187877 by nadovic last updated on 23/Feb/23 $$\mathrm{Simplify}\:\mathrm{completely} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{256}^{−\frac{\mathrm{7}}{\mathrm{16}}} \:×\:\mathrm{128}^{\frac{\mathrm{9}}{\mathrm{28}}} }{\mathrm{512}^{\frac{\mathrm{17}}{\mathrm{36}}} \:×\:\mathrm{64}^{−\frac{\mathrm{11}}{\mathrm{12}}} } \\ $$ Answered by Rasheed.Sindhi last updated on 23/Feb/23…
Question Number 56801 by necx1 last updated on 24/Mar/19 $${The}\:{product}\:{of}\:{three}\:{consecutive}\:{terms} \\ $$$${of}\:\mathrm{4}.\:{The}\:{sum}\:{of}\:{the}\:{GP}\:{is}\:−\frac{\mathrm{7}}{\mathrm{3}}.\:{Find} \\ $$$${the}\:{GP} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Mar/19 $$\boldsymbol{{recheck}}\:\boldsymbol{{the}}\:\boldsymbol{{question}}… \\…
Question Number 187874 by mustafazaheen last updated on 23/Feb/23 $${how}\:{is}\:{solution} \\ $$$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{13}} =\mathrm{x}\:\:\:\:\:\:\:\:\:\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{221}} =? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{x}^{−\mathrm{16}} \left.\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{x}^{−\mathrm{17}} \:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{x}^{\mathrm{221}} \:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right)\mathrm{x}^{\mathrm{21}} \\ $$ Answered by som(math1967) last…
Question Number 56800 by mr W last updated on 24/Mar/19 $${x},{y},{z}\:{are}\:{positive}\:{integers}. \\ $$$${find}\:{all}\:{solutions}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}={xyz}. \\ $$ Commented by MJS last updated on 24/Mar/19 $$\mathrm{with}\:{z}=\mathrm{3}\:\mathrm{we}\:\mathrm{get}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{Fibonacci}\:\mathrm{numbers}…
Question Number 187871 by mustafazaheen last updated on 23/Feb/23 $${how}\:{is}\:{solution} \\ $$$$\mathrm{sgn}\left(\mathrm{cos}\frac{\mathrm{21}}{\mathrm{10}}\right)=? \\ $$ Answered by mr W last updated on 23/Feb/23 $$\frac{\mathrm{21}}{\mathrm{10}}=\mathrm{2}.\mathrm{1}\:>\frac{\pi}{\mathrm{2}}\:{but}\:<\pi \\ $$$$\Rightarrow\mathrm{cos}\:\frac{\mathrm{21}}{\mathrm{10}}\:<\mathrm{0}…
Question Number 187856 by Michaelfaraday last updated on 23/Feb/23 $${find}\:{x} \\ $$$$\mathrm{2}^{\sqrt{{x}}} =\mathrm{8}{x} \\ $$ Answered by mr W last updated on 23/Feb/23 $${t}=\sqrt{{x}}\:>\mathrm{0} \\…
Question Number 187811 by Rupesh123 last updated on 22/Feb/23 Answered by Frix last updated on 22/Feb/23 $${x}^{\mathrm{6}} +\frac{{x}^{\mathrm{5}} }{\mathrm{2}}−\frac{\mathrm{5}{x}^{\mathrm{4}} }{\mathrm{4}}−\frac{\mathrm{5}{x}^{\mathrm{3}} }{\mathrm{8}}+\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{16}}+\frac{\mathrm{5}{x}}{\mathrm{32}}+\frac{\mathrm{1}}{\mathrm{64}}=\mathrm{0} \\ $$$$\mathrm{Try}\:\mathrm{to}\:\mathrm{find}\:\mathrm{2}\:\mathrm{cubic}\:\mathrm{factors}.\:\mathrm{If}\:\mathrm{it}'\mathrm{s}\:\mathrm{possible} \\…