Question Number 140556 by mathsuji last updated on 09/May/21
$${if},\:{m}>\mathrm{0},\:{then}\:{determine}\:{all}\:{real} \\ $$ $${numbers}\:\boldsymbol{{z}}\:{which}\:{satisfy} \\ $$ $$\boldsymbol{{z}}^{\mathrm{2}} \centerdot\left({m}^{\sqrt{\boldsymbol{{z}}}−\boldsymbol{{z}}} \:−\:\mathrm{1}\right)−\sqrt{\boldsymbol{{z}}}+\mathrm{1}=\mathrm{0} \\ $$
Commented byMJS_new last updated on 10/May/21
$${z}\geqslant{t}_{\mathrm{0}} ^{\mathrm{2}} \:\mathrm{with}\:{t}_{\mathrm{0}} \:\mathrm{being}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{root}\:\mathrm{of}\:{t}^{\mathrm{4}} +{t}−\mathrm{1}=\mathrm{0} \\ $$ $${t}_{\mathrm{0}} \approx.\mathrm{724491959001}\:\Rightarrow\:{t}_{\mathrm{0}} ^{\mathrm{2}} \approx.\mathrm{524888599} \\ $$ $$\mathrm{0}\leqslant{m}<\mathrm{1}\:\forall\:{z}\geqslant{t}_{\mathrm{0}} ^{\mathrm{2}} \\ $$
Commented bymathsuji last updated on 10/May/21
$${thankyou}\:{sir} \\ $$