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Category: Algebra

Question-226766

Question Number 226766 by mr W last updated on 13/Dec/25 Answered by mahdipoor last updated on 13/Dec/25 $$\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}+\mathrm{b}\:\Rightarrow \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{1}\:\mathrm{or}\:−\mathrm{2x}−\mathrm{3} \\ $$$$\mathrm{but}\:\mathrm{its}\:\mathrm{only}\:\mathrm{answer}? \\ $$$$\mathrm{all}\:\mathrm{function}\:\mathrm{can}\:\mathrm{show}\:\mathrm{as}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\mathrm{i}=\mathrm{0}} {\overset{\mathrm{m}}…

Find-0-4-dx-1-sin-2-x-

Question Number 226728 by hardmath last updated on 11/Dec/25 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$ Answered by Ghisom_ last updated on 12/Dec/25 $$\mathrm{there}'\mathrm{s}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{but}\:\mathrm{boring}\:\mathrm{solution}\:\mathrm{using} \\ $$$${t}=\mathrm{tan}\:{x}…

If-p-1-x-1-x-2-what-should-p-N-4-D-4-N-4-means-numerator-of-p-in-quaternary-for-x-to-be-777-

Question Number 226713 by ajfour last updated on 11/Dec/25 $$\:\:{If}\: \\ $$$${p}=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$${what}\:{should}\:{p}=\frac{\left({N}\right)_{\mathrm{4}} }{\left({D}\right)_{\mathrm{4}} } \\ $$$$\left({N}\right)_{\mathrm{4}} \:{means}\:{numerator}\:{of}\:{p}\:\:{in} \\ $$$${quaternary}\:{for}\:{x}\:{to}\:{be}\:\mathrm{777}? \\ $$ Terms…

Question-226577

Question Number 226577 by mr W last updated on 06/Dec/25 Answered by Ghisom_ last updated on 06/Dec/25 $${x}_{\mathrm{1}} =\alpha+\sqrt{\beta}+\sqrt{\gamma}+\sqrt{\beta\gamma} \\ $$$${x}_{\mathrm{2}} =\alpha−\sqrt{\beta}−\sqrt{\gamma}+\sqrt{\beta\gamma} \\ $$$${x}_{\mathrm{3}} =\alpha−\sqrt{\beta}+\sqrt{\gamma}−\sqrt{\beta\gamma}…

a-4-b-4-c-4-2d-2-Prove-that-the-equation-has-an-infinite-number-of-natural-solutions-

Question Number 226569 by hardmath last updated on 05/Dec/25 $$\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:=\:\mathrm{2d}^{\mathrm{2}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{solutions} \\ $$ Commented by mr W last updated…