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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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