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Author: Tinku Tara

Question-74720

Question Number 74720 by chess1 last updated on 29/Nov/19 Commented by mathmax by abdo last updated on 29/Nov/19 $${changement}\:\sqrt{\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}}\:={t}\:{give}\:{x}−\mathrm{1}\:={t}^{\mathrm{2}} \left({x}+\mathrm{1}\right)\:\Rightarrow\left(\mathrm{1}−{t}^{\mathrm{2}} \right){x}=\mathrm{1}+{t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}=\frac{\mathrm{1}+{t}^{\mathrm{2}} }{\mathrm{1}−{t}^{\mathrm{2}}…

Question-74716

Question Number 74716 by chess1 last updated on 29/Nov/19 Answered by Tanmay chaudhury last updated on 29/Nov/19 $${x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)×{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)×…{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{25}} }\right)=\mathrm{1} \\ $$$${x}^{\mathrm{25}} ×{A}=\mathrm{1} \\ $$$${x}=\left(\frac{\mathrm{1}}{{A}}\right)^{\frac{\mathrm{1}}{\mathrm{25}}}…

Let-p-and-q-be-positive-integers-having-no-positive-common-divisors-except-unity-Let-z-1-z-2-z-q-be-the-q-values-of-z-p-q-where-z-is-a-fixed-complex-number-Then-the-product-z-1-z-2-z

Question Number 140248 by EnterUsername last updated on 05/May/21 $$\mathrm{Let}\:{p}\:\mathrm{and}\:{q}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{having}\:\mathrm{no}\:\mathrm{positive} \\ $$$$\mathrm{common}\:\mathrm{divisors}\:\mathrm{except}\:\mathrm{unity}.\:\mathrm{Let}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,…,\:{z}_{{q}} \:\mathrm{be}\:\mathrm{the} \\ $$$${q}\:\mathrm{values}\:\mathrm{of}\:{z}^{{p}/{q}} ,\:\mathrm{where}\:{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{complex}\:\mathrm{number}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{product}\:{z}_{\mathrm{1}} {z}_{\mathrm{2}} …{z}_{{q}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{A}\right)\:{z}^{{p}}…

Question-74712

Question Number 74712 by aliesam last updated on 29/Nov/19 Commented by MJS last updated on 29/Nov/19 $$\mathrm{easy}\:\mathrm{solutions} \\ $$$${x}={y}=\mathrm{1} \\ $$$${x}={y}=−\mathrm{2} \\ $$$$\mathrm{no}\:\mathrm{other}\:\mathrm{real}\:\mathrm{solutions} \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right)\:\mathrm{and}\:\mathrm{dividing}\:\mathrm{by}\:{x}^{\mathrm{2}}…

Question-74713

Question Number 74713 by ajfour last updated on 29/Nov/19 Commented by ajfour last updated on 29/Nov/19 $${If}\:{perimeter}\:{of}\:\bigtriangleup{ABC}\:=\:\mathrm{18}\:, \\ $$$${and}\:{area}\:{is}\:{maximum},\:{find} \\ $$$${coordinates}\:{of}\:{points}\:{A},\:{B},\:{C}. \\ $$ Answered by…