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Author: Tinku Tara

If-p-is-a-point-in-the-base-AB-of-a-triangle-ABC-such-that-AP-PB-P-Q-prove-that-p-q-cot-qcot-A-pcot-B-

Question Number 75421 by peter frank last updated on 10/Dec/19 $${If}\:{p}\:{is}\:{a}\:{point}\:{in}\:{the}\:{base} \\ $$$${AB}\:{of}\:\:{a}\:\:{triangle}\:\:{ABC} \\ $$$${such}\:{that}\:{AP}\:\::{PB}={P}:{Q} \\ $$$${prove}\:{that} \\ $$$$\left({p}+{q}\right)\mathrm{cot}\:\theta={q}\mathrm{cot}\:{A}−{p}\mathrm{cot}\:{B} \\ $$ Commented by som(math1967) last…

x-2-2x-3-2-3x-2-6x-9-0-What-is-the-value-of-x-

Question Number 9884 by Joel575 last updated on 12/Jan/17 $$\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{2}} \:+\:\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{9}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:? \\ $$ Answered by sandy_suhendra last updated on 12/Jan/17 $$\left(\mathrm{x}^{\mathrm{2}}…

Question-9880

Question Number 9880 by sandipkd@ last updated on 12/Jan/17 Answered by bansal22luvi@gmail.com last updated on 12/Jan/17 $${let}\:{the}\:{radius}\:{of}\:{smallest}\:{circle}\:{be}\:{r} \\ $$$${CO}=\left(\mathrm{2}−{x}\right) \\ $$$${C}_{\mathrm{1}} {O}=\left(\mathrm{1}+{x}\right) \\ $$$${C}_{\mathrm{1}} {C}=\mathrm{1}…

solve-the-value-of-x-5logx-x-4-

Question Number 9875 by j.masanja06@gmail.com last updated on 11/Jan/17 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\mathrm{5logx}=\frac{\mathrm{x}}{\mathrm{4}} \\ $$ Answered by mrW1 last updated on 12/Jan/17 $$\mathrm{5log}\:{x}=\frac{{x}}{\mathrm{4}} \\ $$$$\mathrm{log}\:{x}=\frac{{x}}{\mathrm{20}} \\…

if-the-eqution-x-3-3hx-q-0-has-the-roots-and-find-the-eqution-with-the-roots-of-i-1-1-1-ii-1-2-1-2-1-2-

Question Number 9874 by j.masanja06@gmail.com last updated on 11/Jan/17 $$\mathrm{if}\:\mathrm{the}\:\mathrm{eqution}\:\mathrm{x}^{\mathrm{3}} +\mathrm{3hx}\:+\:\mathrm{q}=\mathrm{0}\:\mathrm{has}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\alpha,\beta\:\:\mathrm{and}\:\gamma. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{eqution}\:\mathrm{with}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}; \\ $$$$\left(\mathrm{i}\right)\frac{\mathrm{1}}{\alpha\beta}\:+\:\frac{\mathrm{1}}{\beta\gamma}\:+\:\frac{\mathrm{1}}{\alpha\gamma} \\ $$$$\left(\mathrm{ii}\right)\frac{\mathrm{1}}{\alpha^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\beta^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\gamma^{\mathrm{2}} } \\ $$$$ \\…

find-the-relation-between-a-b-c-and-d-if-the-roots-of-the-eqution-ax-3-bx-2-cx-d-0-are-in-i-A-P-ii-G-P-

Question Number 9873 by j.masanja06@gmail.com last updated on 11/Jan/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\:\mathrm{d} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{eqution}\: \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{bx}^{\mathrm{2}} +\mathrm{cx}+\mathrm{d}=\mathrm{0}\:\:\mathrm{are}\:\mathrm{in}; \\ $$$$\left(\mathrm{i}\right)\mathrm{A}.\mathrm{P} \\ $$$$\left(\mathrm{ii}\right)\mathrm{G}.\mathrm{P} \\ $$ Answered by bansal22luvi@gmail.com…

find-the-value-of-n-1-99-n-1-n-2-n-4-a-0-46-and-0-47-b-0-47-and-0-48-c-0-48-and-0-49-d-0-49-and-0-50-kush-

Question Number 9869 by bansal22luvi@gmail.com last updated on 10/Jan/17 $${find}\:{the}\:{value}\:{of} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\:\:\frac{{n}}{\mathrm{1}+{n}^{\mathrm{2}} +{n}^{\mathrm{4}} } \\ $$$$\left.{a}\right)\mathrm{0}.\mathrm{46}\:{and}\:\mathrm{0}.\mathrm{47} \\ $$$$\left.{b}\right)\mathrm{0}.\mathrm{47}\:{and}\:\mathrm{0}.\mathrm{48} \\ $$$$\left.{c}\right)\mathrm{0}.\mathrm{48}\:{and}\:\mathrm{0}.\mathrm{49} \\ $$$$\left.{d}\right)\mathrm{0}.\mathrm{49}\:{and}\:\mathrm{0}.\mathrm{50} \\…