Question Number 224539 by fantastic last updated on 17/Sep/25 $${a}^{{x}} ={m},\:{a}^{{y}} ={n}\:,{a}^{\mathrm{2}} =\left({m}^{{y}} {n}^{{x}} \right)^{{z}} \\ $$$${prove}\:{xyz}=\mathrm{1} \\ $$ Answered by som(math1967) last updated on…
Question Number 224538 by MirHasibulHossain last updated on 17/Sep/25 $$\mathrm{32}^{\mathrm{4r}^{\mathrm{2}} −\mathrm{8}} =\mathrm{1}\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{r}=? \\ $$ Answered by fantastic last updated on 17/Sep/25 $$\left(\mathrm{4}{r}^{\mathrm{2}} −\mathrm{8}\right)=\mathrm{log}\:_{\mathrm{32}} \mathrm{1}=\mathrm{0} \\…
Question Number 224453 by Rojarani last updated on 13/Sep/25 Commented by fantastic last updated on 13/Sep/25 $$−\mathrm{144}? \\ $$ Commented by Rojarani last updated on…
Question Number 224455 by AgniMath last updated on 13/Sep/25 $${If}\:{a},{b},{c}\:\neq\:\mathrm{0}\:{what}\:{is}\:{the}\:{difference} \\ $$$${between}\:{the}\:{maximum}\:{snd}\:{minimum}\: \\ $$$${value}\:{of} \\ $$$${S}\:=\:\mathrm{1}\:+\:\frac{\mid{a}\mid}{{a}}\:+\:\frac{\mathrm{2}\mid{b}\mid}{{b}}\:+\:\frac{\mathrm{3}\mid{ab}\mid}{{ab}}\:−\:\frac{\mathrm{4}\mid{c}\mid}{{c}}\:? \\ $$ Answered by mr W last updated on…
Question Number 224392 by infinityaction last updated on 07/Sep/25 $$\:\:\:\:\:\:\:−\infty<{a}<{b}<\infty\:\:{and}\:\mathrm{0}<\lambda<\mathrm{1}\:\: \\ $$$$\:\:\:\:\:\:\:{x}_{\mathrm{1}} \:=\:{a}\:,\:{x}_{\mathrm{2}} \:=\:{b} \\ $$$$\:\:\:\:\:\:\:\:{x}_{{n}+\mathrm{2}} \:=\:\lambda{x}_{{n}} \:+\:\left(\mathrm{1}−\lambda\right){x}_{{n}+\mathrm{1}} \:\:\forall\:{n}\:\in\:\mathbb{N} \\ $$$$\:\:\mathrm{find}\:\:{x}_{{n}\:} \:=\:?\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\…
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Question Number 224342 by Rojarani last updated on 04/Sep/25 Answered by mingski last updated on 04/Sep/25 $${x}^{\mathrm{2}} −{x}−\mathrm{1000}\sqrt{\mathrm{1}+\mathrm{8000}{x}}=\mathrm{1000} \\ $$$${x}^{\mathrm{2}} −{x}=\mathrm{1000}\left(\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{8000}{x}}\right) \\ $$$${x}\left({x}−\mathrm{1}\right)=\mathrm{1000}\left(\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{8000}{x}}\right) \\ $$$$\mathrm{Then}\:\mathrm{guess}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}.…
Question Number 224331 by hardmath last updated on 03/Sep/25 $$\mathrm{a},\mathrm{b},\mathrm{c}\:>\:\mathrm{0} \\ $$$$\mathrm{prove}\:\mathrm{that} \\ $$$$\Sigma\:\mathrm{a}^{\mathrm{2}} \:\geqslant\:\Sigma\:\mathrm{ab}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:\Sigma\:\left(\mid\mathrm{a}−\mathrm{c}\mid\:+\:\mid\mathrm{b}−\mathrm{c}\mid\right)^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 224312 by behi834171 last updated on 01/Sep/25 Answered by Frix last updated on 01/Sep/25 $${x}_{\mathrm{1}} ={c}+\sqrt{{a}}+\sqrt{{b}}+\sqrt{{ab}} \\ $$$${x}_{\mathrm{2}} ={c}+\sqrt{{a}}−\sqrt{{b}}−\sqrt{{ab}} \\ $$$${x}_{\mathrm{3}} ={c}−\sqrt{{a}}+\sqrt{{b}}−\sqrt{{ab}} \\…
Question Number 224234 by MirHasibulHossain last updated on 27/Aug/25 $$\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\mathrm{7} \\ $$$$\sqrt{\mathrm{x}+\mathrm{y}}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{x},\mathrm{y}\right). \\ $$ Answered by Frix last updated on 27/Aug/25 $$\mathrm{With}\:\mathrm{these}\:\mathrm{numbers}\:\mathrm{it}'\mathrm{s}\:\mathrm{obvious}: \\…