Question Number 151073 by mathdanisur last updated on 18/Aug/21 $$\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\begin{pmatrix}{\mathrm{50}}\\{\mathrm{0}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{1}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{2}}\end{pmatrix}^{\mathrm{2}} +…+\begin{pmatrix}{\mathrm{50}}\\{\mathrm{49}}\end{pmatrix}^{\mathrm{2}} +\begin{pmatrix}{\mathrm{50}}\\{\mathrm{50}}\end{pmatrix}^{\mathrm{2}} \\ $$ Answered by ArielVyny last updated on 18/Aug/21…
Question Number 85532 by oustmuchiya@gmail.com last updated on 22/Mar/20 $${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$ Answered by mind is power last updated on 22/Mar/20 $$\left(\mathrm{2}{a}−\frac{\mathrm{1}}{\mathrm{2}{a}}\right)^{{k}} \\ $$$$=\underset{{i}=\mathrm{0}} {\overset{{k}}…
Question Number 151070 by mathdanisur last updated on 18/Aug/21 $$\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{30}\:\:\:\mathrm{and}\:\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}} \\ $$ Commented by john_santu last updated on 18/Aug/21 $$\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}+\frac{\mathrm{1}}{\mathrm{c}}\geqslant\frac{\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}=\frac{\mathrm{9}}{\mathrm{30}}=\frac{\mathrm{3}}{\mathrm{10}}…
Question Number 151059 by john_santu last updated on 18/Aug/21 $$\:\:\:\:\sqrt[{\mathrm{3}}]{\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:+\mathrm{2}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{2}−\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{2}}}\:=\:\mathrm{2}\: \\ $$$$\:\:\:\:\mathrm{x}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151052 by mathdanisur last updated on 17/Aug/21 $$\mathrm{if}\:\:\:\mathrm{a};\mathrm{b};\mathrm{c}\:\:\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}\:\:\mathrm{and} \\ $$$$\frac{\mathrm{a}}{\mathrm{1}+\mathrm{a}}\:+\:\frac{\mathrm{b}}{\mathrm{1}+\mathrm{b}}\:+\:\frac{\mathrm{c}}{\mathrm{1}+\mathrm{c}}\:=\:\mathrm{1}\:\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{abc}\:\leqslant\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$ Answered by dumitrel last updated on 18/Aug/21 $$\mathrm{3}{r}+\mathrm{2}{q}+{p}=\mathrm{1}+{p}+{q}+{r}\Rightarrow\mathrm{2}{r}+{q}=\mathrm{1} \\…
Question Number 151045 by mathdanisur last updated on 17/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151042 by mathdanisur last updated on 17/Aug/21 $$\mathrm{if}\:\:\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\mathrm{1}}\:+\:\sqrt{\sqrt[{\mathrm{3}}]{\mathrm{16}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{4}}}\:=\:\sqrt{\boldsymbol{\mathrm{x}}}\:\:;\:\:\boldsymbol{\mathrm{x}}\in\mathbb{Z} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Commented by MJS_new last updated on 18/Aug/21 $${x}\notin\mathbb{Z} \\ $$ Terms…
Question Number 151043 by mathdanisur last updated on 17/Aug/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}: \\ $$$$\begin{cases}{\boldsymbol{\mathrm{y}}\:=\:\frac{\mathrm{2x}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\\{\boldsymbol{\mathrm{z}}\:=\:\frac{\mathrm{2y}}{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }}\\{\boldsymbol{\mathrm{x}}\:=\:\frac{\mathrm{2z}}{\mathrm{1}−\mathrm{z}^{\mathrm{2}} }}\end{cases} \\ $$ Answered by john_santu last updated on 18/Aug/21 $$\mathrm{x}=\mathrm{y}=\mathrm{z}\:\Rightarrow\mathrm{x}=\frac{\mathrm{2x}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…
Question Number 151035 by text last updated on 17/Aug/21 $$\begin{vmatrix}{}&{}\\{}&{}\end{vmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85490 by oustmuchiya@gmail.com last updated on 22/Mar/20 $${Given}\:{that}\:{the}\:{expression}\:\mathrm{2}{x}^{\mathrm{3}} +{px}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{9}\:{is}\:{exactly}\:{divisable}\:{by}\:{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5},\:{find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{q}}.\:{Hence}\:{factorise}\:{the}\:{expression}\:{fully} \\ $$ Commented by john santu last updated on 22/Mar/20 $${nothing}\:{q}\:{in}\:{this}\:{equation}. \\…