if, m>0, then determine all real numbers z which satisfy z^2 ∙(m^((√z)−z) − 1)−(√z)+1=0


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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 byMJS_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 bymathsuji last updated on 10/May/21

$t h a n k y o u s i r$
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