if-m-gt-0-then-determine-all-real-numbers-z-which-satisfy-z-2-m-z-z-1-z-1-0-

Question Number 140556 by mathsuji last updated on 09/May/21

i f, m > 0, t h e n d e t e r m i n e a l l r e a l

n u m b e r s z w h i c h s a t i s f y

z^{2} \cdot (m^{\sqrt{z} - z} - 1) - \sqrt{z} + 1 = 0

Commented by MJS_new last updated on 10/May/21

z ⩾ t_{0}^{2} with t_{0} being the positive root of t^{4} + t - 1 = 0

t_{0} \approx . 724491959001 \Rightarrow t_{0}^{2} \approx . 524888599

0 ⩽ m < 1 \forall z ⩾ t_{0}^{2}

Commented by mathsuji last updated on 10/May/21

t h a n k y o u s i r