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Category: Algebra

If-x-7-4-3-Find-x-4-x-3-9x-2-2x-5-x-2-4x-3-

Question Number 199550 by hardmath last updated on 05/Nov/23 $$\mathrm{If} \\ $$$$\mathrm{x}\:=\:\sqrt{\mathrm{7}\:+\:\mathrm{4}\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}^{\mathrm{4}} \:−\:\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{9x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{5}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}}\:\:=\:\:? \\ $$ Answered by Rasheed.Sindhi…

Question-199547

Question Number 199547 by hardmath last updated on 05/Nov/23 Answered by mr W last updated on 05/Nov/23 $$\left.\mathrm{1}\right) \\ $$$${n}×{n}!=\left({n}+\mathrm{1}−\mathrm{1}\right)×{n}!=\left({n}+\mathrm{1}\right)!−{n}! \\ $$$$\mathrm{1}×\mathrm{1}!+\mathrm{2}×\mathrm{2}!+…+\mathrm{2022}×\mathrm{2022}! \\ $$$$=\mathrm{2}!−\mathrm{1}!+\mathrm{3}!−\mathrm{2}!+….+\mathrm{2023}!−\mathrm{2022}! \\…

2-7-12-x-270-Find-x-

Question Number 199602 by hardmath last updated on 05/Nov/23 $$\mathrm{2}\:+\:\mathrm{7}\:+\:\mathrm{12}\:+\:…\:+\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{270} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 06/Nov/23 $${a}=\mathrm{2},{d}=\mathrm{5} \\ $$$${S}_{{n}} =\frac{{n}}{\mathrm{2}}\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right)…

if-a-n-is-geometric-sequence-and-we-know-p-n-m-2-S-p-f-a-n-a-m-n-m-Attention-The-purpose-of-obtaining-a-relationship-without-the-need-for-direct-calculation-is-the-common-rat

Question Number 199593 by jabarsing last updated on 05/Nov/23 $${if}\:\left\{{a}_{{n}} \right\}\:{is}\:{geometric}\:{sequence}\:{and}\: \\ $$$$ \\ $$$${we}\:{know}\:,\:{p}=\frac{{n}+{m}}{\mathrm{2}}\:\:\Rightarrow \\ $$$$\:{S}_{{p}} \:=\:{f}\left({a}_{{n}} ,{a}_{{m}} ,{n},{m}\right)=? \\ $$$$\blacksquare{Attention}:\: \\ $$The purpose…

Solve-100-x-200-

Question Number 199486 by hardmath last updated on 04/Nov/23 $$\mathrm{Solve}:\:\:\:\mathrm{100}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{200} \\ $$ Answered by cortano12 last updated on 04/Nov/23 $$\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{100}^{\mathrm{x}} \right)=\:\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{200}\right) \\…

can-someone-factor-this-3x-3-y-7x-2-5xy-3-y-2-

Question Number 199482 by York12 last updated on 04/Nov/23 $$\mathrm{can}\:\mathrm{someone}\:\mathrm{factor}\:\mathrm{this}\:\left(\mathrm{3x}^{\mathrm{3}} \mathrm{y}−\mathrm{7x}^{\mathrm{2}} +\mathrm{5xy}^{\mathrm{3}} −\mathrm{y}^{\mathrm{2}} \right) \\ $$ Commented by Frix last updated on 04/Nov/23 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{this}\:\mathrm{is}\:\mathrm{possible}. \\…