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Question Number 113393 by Her_Majesty last updated on 13/Sep/20
loving questions of the form  “if ... then find the sum/product/etc. of...  so please solve these:  (1)  if γ and λ are the solutions of  x^2 +x−12=0 then find coshλ−cotγ  (2)  if a+b=2 and a−b=0 then find  ∫x^((a+b)/(2ab)) ln(−e^(iπa) −x)ln(e^(cos^(−1) b) −x)dx  are you intelligent enough?  then please please please sir or madam  help me!!! I need an answer urgentliest!!!!  good luck!  (c) by HeR MaJε∫tY  20200913
$${loving}\:{questions}\:{of}\:{the}\:{form} \\ $$$$“{if}\:…\:{then}\:{find}\:{the}\:{sum}/{product}/{etc}.\:{of}… \\ $$$${so}\:{please}\:{solve}\:{these}: \\ $$$$\left(\mathrm{1}\right) \\ $$$${if}\:\gamma\:{and}\:\lambda\:{are}\:{the}\:{solutions}\:{of} \\ $$$${x}^{\mathrm{2}} +{x}−\mathrm{12}=\mathrm{0}\:{then}\:{find}\:{cosh}\lambda−{cot}\gamma \\ $$$$\left(\mathrm{2}\right) \\ $$$${if}\:{a}+{b}=\mathrm{2}\:{and}\:{a}−{b}=\mathrm{0}\:{then}\:{find} \\ $$$$\int{x}^{\frac{{a}+{b}}{\mathrm{2}{ab}}} {ln}\left(−{e}^{{i}\pi{a}} −{x}\right){ln}\left({e}^{{cos}^{−\mathrm{1}} {b}} −{x}\right){dx} \\ $$$${are}\:{you}\:{intelligent}\:{enough}? \\ $$$${then}\:{please}\:{please}\:{please}\:{sir}\:{or}\:{madam} \\ $$$${help}\:{me}!!!\:{I}\:{need}\:{an}\:{answer}\:\boldsymbol{\mathrm{urgentliest}}!!!! \\ $$$${good}\:{luck}! \\ $$$$\left({c}\right)\:{by}\:\mathbb{H}\mathfrak{e}\mathscr{R}\:\mathfrak{M}\boldsymbol{{a}}\mathbb{J}\epsilon\int{t}\mathscr{Y}\:\:\mathrm{20200913} \\ $$
Commented by john santu last updated on 13/Sep/20
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Commented by malwaan last updated on 13/Sep/20
x^2 +x−12=0  ⇒(x−3)(x+4)=0  ∴ solution set = {3;−4}  (i)γ=3;λ=−4⇒cosh(−4)−cot(3)=34.32349  (ii)γ=−4;λ=3⇒cosh(3)−cot(−4)=10.93135
$${x}^{\mathrm{2}} +{x}−\mathrm{12}=\mathrm{0} \\ $$$$\Rightarrow\left({x}−\mathrm{3}\right)\left({x}+\mathrm{4}\right)=\mathrm{0} \\ $$$$\therefore\:{solution}\:{set}\:=\:\left\{\mathrm{3};−\mathrm{4}\right\} \\ $$$$\left({i}\right)\gamma=\mathrm{3};\lambda=−\mathrm{4}\Rightarrow{cosh}\left(−\mathrm{4}\right)−{cot}\left(\mathrm{3}\right)=\mathrm{34}.\mathrm{32349} \\ $$$$\left({ii}\right)\gamma=−\mathrm{4};\lambda=\mathrm{3}\Rightarrow{cosh}\left(\mathrm{3}\right)−{cot}\left(−\mathrm{4}\right)=\mathrm{10}.\mathrm{93135} \\ $$
Commented by malwaan last updated on 13/Sep/20
(2)a+b=2 ; a−b=0  ⇒a=1 ; b=1  ∴ ∫x ln(1−x)ln(1−x)dx=  ∫x[ln(1−x)]^2 dx=...
$$\left(\mathrm{2}\right){a}+{b}=\mathrm{2}\:;\:{a}−{b}=\mathrm{0} \\ $$$$\Rightarrow{a}=\mathrm{1}\:;\:{b}=\mathrm{1} \\ $$$$\therefore\:\int{x}\:{ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−{x}\right){dx}= \\ $$$$\int{x}\left[{ln}\left(\mathrm{1}−{x}\right)\right]^{\mathrm{2}} {dx}=… \\ $$
Commented by Rasheed.Sindhi last updated on 13/Sep/20
Perhaps Her Majesty wanted to  give a message!
$${Perhaps}\:{Her}\:{Majesty}\:{wanted}\:{to} \\ $$$${give}\:{a}\:{message}! \\ $$
Commented by malwan last updated on 13/Sep/20
what is the point please ?  I am sure you don^, t need help  but we[at least me]do
$${what}\:{is}\:{the}\:{point}\:{please}\:? \\ $$$${I}\:{am}\:{sure}\:{you}\:{don}^{,} {t}\:{need}\:{help} \\ $$$${but}\:{we}\left[{at}\:{least}\:{me}\right]{do} \\ $$$$ \\ $$
Commented by Her_Majesty last updated on 13/Sep/20
one point is,  (you post a question) ⇒ (you need help)  no need to post the same question over and  over again. l  another point is, people who post questions  to show us we are unable to solve them while  they themselves are able to, ruin the forum.  a 3^(rd)  point is, it′s useless to solve i.e. a  polynome and ask for i.e. “7x_1 −13x_2 +1/x_3 ”  because there′s no takeaway from this.  indeed there is if you ask for “1/x_1 +1/x_2 +  +1/x_3 ”... ⇒ ∃(silly questions)  4^(th) . if you post something today everybody  can see it was YOU and TODAY. no need to  state these facts again.
$${one}\:{point}\:{is}, \\ $$$$\left({you}\:{post}\:{a}\:{question}\right)\:\Rightarrow\:\left({you}\:{need}\:{help}\right) \\ $$$${no}\:{need}\:{to}\:{post}\:{the}\:{same}\:{question}\:{over}\:{and} \\ $$$${over}\:{again}.\:{l} \\ $$$${another}\:{point}\:{is},\:{people}\:{who}\:{post}\:{questions} \\ $$$${to}\:{show}\:{us}\:{we}\:{are}\:{unable}\:{to}\:{solve}\:{them}\:{while} \\ $$$${they}\:{themselves}\:{are}\:{able}\:{to},\:{ruin}\:{the}\:{forum}. \\ $$$${a}\:\mathrm{3}^{{rd}} \:{point}\:{is},\:{it}'{s}\:{useless}\:{to}\:{solve}\:{i}.{e}.\:{a} \\ $$$${polynome}\:{and}\:{ask}\:{for}\:{i}.{e}.\:“\mathrm{7}{x}_{\mathrm{1}} −\mathrm{13}{x}_{\mathrm{2}} +\mathrm{1}/{x}_{\mathrm{3}} '' \\ $$$${because}\:{there}'{s}\:{no}\:{takeaway}\:{from}\:{this}. \\ $$$${indeed}\:{there}\:{is}\:{if}\:{you}\:{ask}\:{for}\:“\mathrm{1}/{x}_{\mathrm{1}} +\mathrm{1}/{x}_{\mathrm{2}} + \\ $$$$+\mathrm{1}/{x}_{\mathrm{3}} ''…\:\Rightarrow\:\exists\left({silly}\:{questions}\right) \\ $$$$\mathrm{4}^{{th}} .\:{if}\:{you}\:{post}\:{something}\:{today}\:{everybody} \\ $$$${can}\:{see}\:{it}\:{was}\:{YOU}\:{and}\:{TODAY}.\:{no}\:{need}\:{to} \\ $$$${state}\:{these}\:{facts}\:{again}. \\ $$

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