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Category: Algebra

Three-numbers-are-in-G-P-such-that-their-sum-is-p-and-the-sum-of-their-square-is-q-Find-the-middle-term-of-the-G-P-

Question Number 55893 by Tawa1 last updated on 05/Mar/19 $$\mathrm{Three}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{G}.\mathrm{P}\:\mathrm{such}\:\mathrm{that}\:\mathrm{their}\:\mathrm{sum}\:\mathrm{is}\:\:\boldsymbol{\mathrm{p}}\:\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{square}\:\mathrm{is}\:\:\boldsymbol{\mathrm{q}}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P} \\ $$ Answered by kaivan.ahmadi last updated on 05/Mar/19 $${let}\:{a},{b},{c}\:{are}\:{numbers},\:{so} \\ $$$${b}^{\mathrm{2}} ={ac}.…

a-b-2-bc-c-2-b-a-2-ac-c-2-c-a-2-ab-b-2-solve-for-a-b-c-

Question Number 55889 by behi83417@gmail.com last updated on 05/Mar/19 $$\:\:\:\:\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{bc}}+\boldsymbol{\mathrm{c}}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{ac}}+\boldsymbol{\mathrm{c}}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{c}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{ab}}+\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\::\:\:\boldsymbol{\mathrm{a}},\:\:\boldsymbol{\mathrm{b}},\:\:\boldsymbol{\mathrm{c}}. \\ $$ Answered by MJS last…

a-1-b-b-2-b-1-c-c-2-c-ab-a-2-b-2-solve-for-a-b-c-

Question Number 55888 by behi83417@gmail.com last updated on 05/Mar/19 $$\:\:\:\boldsymbol{\mathrm{a}}=\mathrm{1}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\mathrm{b}}=\mathrm{1}+\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{c}}^{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\mathrm{c}}=\boldsymbol{\mathrm{ab}}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\::\:\:\boldsymbol{\mathrm{a}},\:\:\boldsymbol{\mathrm{b}},\:\:\boldsymbol{\mathrm{c}}. \\ $$ Answered by MJS last updated on…

x-4-2-2-x-2-x-2-2-0-x-

Question Number 121423 by Jamshidbek2311 last updated on 08/Nov/20 $${x}^{\mathrm{4}} −\mathrm{2}\sqrt{\mathrm{2}}{x}^{\mathrm{2}} −{x}+\mathrm{2}−\sqrt{\mathrm{2}}=\mathrm{0}\:\:\:{x}=? \\ $$ Answered by 2004 last updated on 08/Nov/20 $$\sqrt{\mathrm{2}}=\mathrm{t} \\ $$$$\mathrm{t}^{\mathrm{2}} −\mathrm{t}\left(\mathrm{2x}^{\mathrm{2}}…

a-2-1-b-2-b-2-c-2-b-4-ab-c-solve-for-a-b-c-

Question Number 55887 by behi83417@gmail.com last updated on 05/Mar/19 $$\:\:\:{a}^{\mathrm{2}} +\mathrm{1}={b}^{\mathrm{2}} \\ $$$$\:\:\:{b}^{\mathrm{2}} +{c}^{\mathrm{2}} ={b}^{\mathrm{4}} \\ $$$$\:\:\:{ab}={c} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\::\:\:\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}},\:\boldsymbol{\mathrm{c}}. \\ $$ Answered by MJS last…