Menu Close

Author: Tinku Tara

The-coefficient-of-x-2-in-the-expansion-of-1-2-p-x-5-1-px-6-is-70-Find-the-possible-values-of-the-constant-p-

Question Number 226053 by Linton last updated on 18/Nov/25 $${The}\:{coefficient}\:{of}\:{x}^{\mathrm{2}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\:\left(\mathrm{2}/{p}\right){x}\right)^{\mathrm{5}} \:+\:\left(\mathrm{1}+{px}\right)^{\mathrm{6}} \:{is}\:\mathrm{70}. \\ $$$${Find}\:{the}\:{possible}\:{values}\:{of}\:{the} \\ $$$${constant}\:{p}. \\ $$ Answered by mr W…

Question-225994

Question Number 225994 by Spillover last updated on 17/Nov/25 Answered by Simurdiera last updated on 18/Nov/25 $${Soluci}\acute {{o}n} \\ $$$$\int_{\mathrm{1}/\mathrm{2}} ^{\:\mathrm{1}} \frac{\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }}{{x}\centerdot\mathrm{sin}\left(\mathrm{arccos}\left({x}\right)\right)\:+\:\mathrm{arcsin}\left({x}\right)}\centerdot\frac{\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }}\:{dx}…

2-100-2-100-lt-or-gt-

Question Number 225970 by fantastic2 last updated on 17/Nov/25 $$\mathrm{2}^{\mathrm{100}!} \:?\:\mathrm{2}^{\mathrm{100}} !\left[=,<{or}\:>\right] \\ $$ Commented by Ghisom_ last updated on 18/Nov/25 $${b}^{{n}!} \:\mathrm{vs}.\:{b}^{{n}} !\:\:\mathrm{where}\:{b},\:{n}\:\in\mathbb{N}\wedge{b}\geqslant\mathrm{2} \\…