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Author: Tinku Tara

Solve-by-computer-programming-a-b-amp-c-are-Prime-numbers-And-they-are-in-AP-and-d-is-common-difference-Example-a-b-c-d-3-5-7-2-Just-Next-Set-a-b-c-d-

Question Number 202058 by BaliramKumar last updated on 19/Dec/23 $$\mathrm{Solve}\:\mathrm{by}\:\mathrm{computer}\:\mathrm{programming} \\ $$$${a},\:{b}\:\&\:{c}\:{are}\:{Prime}\:{numbers}.\:\mathrm{And}\:\mathrm{they} \\ $$$$\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{and}\:\mathrm{d}\:\mathrm{is}\:\mathrm{common}\:\mathrm{difference} \\ $$$$\mathrm{Example}\:\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:\left(\mathrm{3},\:\mathrm{5},\:\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\mathrm{Just}\:\mathrm{Next}\:\mathrm{Set}\left(\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\right)\:=\:? \\ $$ Commented by BaliramKumar last updated…

Question-202082

Question Number 202082 by Abduljalal last updated on 19/Dec/23 Answered by AST last updated on 20/Dec/23 $${p}^{\mathrm{2}} −{p}−\mathrm{2}=\mathrm{0}\left({p}={x}^{\mathrm{3}} \right)\Rightarrow{p}=\mathrm{2}\:{or}\:−\mathrm{1} \\ $$$$\Rightarrow{x}^{\mathrm{3}} =\mathrm{2}\:{or}\:{x}^{\mathrm{3}} =−\mathrm{1}\Rightarrow{x}=\sqrt[{\mathrm{3}}]{\mathrm{2}};\sqrt[{\mathrm{3}}]{\mathrm{2}}{e}^{\frac{\mathrm{2}{i}\pi}{\mathrm{3}}} ,\sqrt[{\mathrm{3}}]{\mathrm{2}}{e}^{\frac{\mathrm{4}\pi{i}}{\mathrm{3}}} \\…

If-a-circle-of-radius-r-is-inscribed-in-a-triangl-ABC-Express-r-in-terms-of-a-b-and-c-only-

Question Number 202001 by necx122 last updated on 18/Dec/23 $${If}\:{a}\:{circle}\:{of}\:{radius}\:{r}\:{is}\:{inscribed}\:{in} \\ $$$${a}\:{triangl}\:{ABC}.\:{Express}\:{r}\:{in}\:{terms}\:{of} \\ $$$${a},{b}\:{and}\:{c}\:{only} \\ $$ Answered by AST last updated on 18/Dec/23 $${r}=\frac{\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}}{{s}}\:{where}\:{s}=\frac{{a}+{b}+{c}}{\mathrm{2}} \\…