Menu Close

Category: Algebra

lim-x-x-1-x-where-is-a-fractional-part-of-x-

Tinku Tara 0 Comments

Question Number 205174 by universe last updated on 12/Mar/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left\{{x}^{\mathrm{1}/{x}} \right\}\:=\:?\:{where}\:\left\{.\right\}\:{is}\:{a}\:{fractional}\:{part}\:{of}\:{x} \\ $$ Answered by lepuissantcedricjunior last updated on 12/Mar/24 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\boldsymbol{{x}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} =\infty^{\mathrm{0}} =\boldsymbol{\mathrm{F}{I}}…

Read more →

If-x-y-z-gt-0-then-in-ABC-holds-yz-h-a-2-R-2-4F-2-x-y-z-2-

Tinku Tara 0 Comments

Question Number 205203 by hardmath last updated on 12/Mar/24 $$\mathrm{If}\:\:\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{in}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Sigma\:\:\frac{\mathrm{yz}}{\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} }\:\:\leqslant\:\:\frac{\mathrm{R}^{\mathrm{2}} }{\mathrm{4F}^{\mathrm{2}} }\:\:\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Read more →

Find-the-determinant-determinant-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-

Tinku Tara 0 Comments

Question Number 205155 by depressiveshrek last updated on 10/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−\lambda}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}−\lambda}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}−\lambda}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}−\lambda}\end{vmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Read more →

let-x-2-3x-p-0-has-two-positive-roots-a-and-b-then-inf-4-a-1-b-is-

Tinku Tara 0 Comments

Question Number 205116 by universe last updated on 09/Mar/24 $$\:\:\mathrm{let}\:\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{p}\:=\:\mathrm{0}\:\mathrm{has}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{roots} \\ $$$$\:'\mathrm{a}'\:\mathrm{and}\:'\mathrm{b}'\:\mathrm{then}\:\:\mathrm{inf}\left(\frac{\mathrm{4}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}\right)\:\mathrm{is}\: \\ $$ Answered by pi314 last updated on 09/Mar/24 $$\frac{\mathrm{4}{b}+{a}}{{ab}}=\frac{\mathrm{3}+\mathrm{3}{b}}{{p}} \\ $$$$\mathrm{9}−\mathrm{4}{p}\geqslant\mathrm{0};{p}\leqslant\frac{\mathrm{9}}{\mathrm{4}}…

Read more →

given-that-there-are-real-constant-a-b-c-d-such-the-identity-x-2-2xy-y-2-ax-by-2-cx-dy-2-holds-for-all-x-y-R-this-implies-a-5-b-1-c-0-lt-lt-1-

Tinku Tara 0 Comments

Question Number 205101 by universe last updated on 08/Mar/24 $$\:\:\mathrm{given}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{real}\:\mathrm{constant}\:\mathrm{a},\mathrm{b},\:\mathrm{c},\:\mathrm{d} \\ $$$$\:\:\mathrm{such}\:\mathrm{the}\:\mathrm{identity} \\ $$$$\:\lambda\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} =\:\left(\mathrm{ax}+\mathrm{by}\right)^{\mathrm{2}} +\left(\mathrm{cx}+\mathrm{dy}\right)^{\mathrm{2}} \:\mathrm{holds} \\ $$$$\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\:\in\:\mathbb{R}\:\mathrm{this}\:\mathrm{implies} \\ $$$$\left({a}\right)\:\lambda=−\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\lambda\geqslant\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\mathrm{0}<\lambda<\mathrm{1} \\ $$$$\:\left({d}\right)\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{such}\:\lambda\in\mathbb{R} \\…

Read more →

Question-205092

Tinku Tara 0 Comments

Question Number 205092 by BaliramKumar last updated on 08/Mar/24 Answered by A5T last updated on 08/Mar/24 $${n}^{\mathrm{2}} +\mathrm{19}{n}+\mathrm{92}−{x}^{\mathrm{2}} =\mathrm{0} \\ $$$${n}=\frac{−\mathrm{19}\underset{−} {+}\sqrt{\mathrm{361}−\mathrm{4}\left(\mathrm{92}−{x}^{\mathrm{2}} \right)}}{\mathrm{2}}=\frac{−\mathrm{19}\underset{−} {+}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{7}}}{\mathrm{2}}…

Read more →