Question Number 147011 by mathdanisur last updated on 17/Jul/21
$$\mathrm{2}{x}\:-\:\sqrt{\mathrm{2}{x}\:-\:\mathrm{3}}\:-\:\mathrm{9}\:=\:\mathrm{0} \\ $$$${if}\:{there}'{s}\:\boldsymbol{{a}}\:{solution}\:{to}\:{equation}, \\ $$$${find}\:\:\mathrm{4}\boldsymbol{{a}}\:+\:\mathrm{3}\:=\:? \\ $$
Commented by 7770 last updated on 17/Jul/21
$$\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{36}\boldsymbol{{x}}+\mathrm{81}−\mathrm{2}\boldsymbol{{x}}+\mathrm{3}=\mathrm{0} \\ $$$$\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{38}\boldsymbol{{x}}+\mathrm{84}=\mathrm{0} \\ $$$$\:\boldsymbol{{x}}_{\mathrm{1}} =\mathrm{6}\:\:\:\:\:\:\boldsymbol{{x}}_{\mathrm{2}} =\mathrm{3}.\mathrm{5} \\ $$$$\:\therefore\:\mathrm{4}\left(\mathrm{3}.\mathrm{5}\right)+\mathrm{3}=\mathrm{17} \\ $$$$\:\:\:\:\:\mathrm{4}\left(\mathrm{6}\right)+\mathrm{3}=\mathrm{27} \\ $$
Commented by otchereabdullai@gmail.com last updated on 18/Jul/21
$$\mathrm{nice}\:\mathrm{question} \\ $$
Commented by mathdanisur last updated on 18/Jul/21
$${thank}\:{you}\:{Ser} \\ $$
Answered by gsk2684 last updated on 17/Jul/21
$$\left(\sqrt{\mathrm{2}{a}−\mathrm{3}}\right)^{\mathrm{2}} −\sqrt{\mathrm{2}{a}−\mathrm{3}}−\mathrm{6}=\mathrm{0} \\ $$$${t}^{\mathrm{2}} −{t}−\mathrm{6}=\mathrm{0} \\ $$$$\left({t}−\mathrm{3}\right)\left({t}+\mathrm{2}\right)=\mathrm{0} \\ $$$${t}=\mathrm{3}\: \\ $$$$\sqrt{\mathrm{2}{a}−\mathrm{3}}=\mathrm{3} \\ $$$$\mathrm{2}{a}=\mathrm{12} \\ $$$$\mathrm{4}{a}+\mathrm{3}=\mathrm{27} \\ $$
Commented by mathdanisur last updated on 17/Jul/21
$${thankyou}\:{Ser},\:{but}\:{answer}\:\mathrm{17} \\ $$
Commented by gsk2684 last updated on 17/Jul/21
$${if}\:{so}\:{then}\:{a}=\frac{\mathrm{17}−\mathrm{3}}{\mathrm{4}}=\frac{\mathrm{14}}{\mathrm{4}}=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$\mathrm{2}{a}−\sqrt{\mathrm{2}{a}−\mathrm{3}}−\mathrm{9} \\ $$$$\mathrm{7}−\mathrm{2}−\mathrm{9} \\ $$$$\neq\mathrm{0} \\ $$
Commented by mathdanisur last updated on 18/Jul/21
$${thank}\:{you}\:{Ser} \\ $$
Answered by Rasheed.Sindhi last updated on 17/Jul/21
$$\mathrm{2}{x}\:-\:\sqrt{\mathrm{2}{x}\:-\:\mathrm{3}}\:-\:\mathrm{9}\:=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\underset{−} {\mathrm{4}\boldsymbol{{a}}+\mathrm{3}=?\:\boldsymbol{{a}}:\:{solution}\:{to}\:{the}\:{equation}} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{36}{x}+\mathrm{81}=\mathrm{2}{x}−\mathrm{3} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{38}{x}+\mathrm{84}=\mathrm{0} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{19}{x}+\mathrm{42}=\mathrm{0} \\ $$$$\left({x}−\mathrm{6}\right)\left(\mathrm{2}{x}−\mathrm{7}\right)=\mathrm{0} \\ $$$${x}=\mathrm{6}\:\vee\:{x}=\mathrm{7}/\mathrm{2}\:\left(\mathcal{E}{xtaneous}\:{root}\right) \\ $$$$\boldsymbol{{a}}=\mathrm{6} \\ $$$$\mathrm{4}\boldsymbol{{a}}+\mathrm{3}=\mathrm{4}\left(\mathrm{6}\right)+\mathrm{3}=\mathrm{27} \\ $$$$\left(\:{If}\:{x}=\mathrm{7}/\mathrm{2}\:\boldsymbol{{were}}\:\boldsymbol{{satisfied}}\:\right. \\ $$$$\left.{then}\:\mathrm{4}\boldsymbol{{a}}+\mathrm{3}=\mathrm{4}\left(\frac{\mathrm{7}}{\mathrm{2}}\right)+\mathrm{3}=\mathrm{17}\:\right) \\ $$
Commented by mathdanisur last updated on 17/Jul/21
$${thank}\:{you}\:{Ser} \\ $$
Commented by mathdanisur last updated on 18/Jul/21
$${thank}\:{you}\:{Ser} \\ $$