for p,q∈R satisfying p^4 +q^4 =4pq find the range of p+q when 1) no restriction 2) 0≤p≤1, 0≤q≤1


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Question Number 138235 by mr W last updated on 11/Apr/21

$f o r p, q \in R s a t i s f y i n g p^{4} + q^{4} = 4 p q$ $f i n d t h e r a n g e o f p + q w h e n$ $1) n o r e s t r i c t i o n$ $2) 0 ⩽ p ⩽ 1, 0 ⩽ q ⩽ 1$
	Answered by mr W last updated on 12/Apr/21

	Commented by mr W last updated on 12/Apr/21

	$p + q = k$ $1) w i t h o u t r e s t r i c t i o n$ $k_{m a x} = 2 \sqrt{2}$ $k_{m i n} = - 2 \sqrt{2}$ $2) w i t h r e s t r i c t i o n : 0 ⩽ p, q ⩽ 1$ $k_{m a x} \approx 1.25099$ $k_{m i n} = 0$
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