if-a-lt-b-lt-0-and-a-4-2a-2-b-2-b-4-a-4-2a-2-b-2-b-4-

Question Number 200729 by mnjuly1970 last updated on 22/Nov/23

i f a < b < 0

a n d \sqrt{a^{4} + 2 a^{2} b^{2} + b^{4}} + \sqrt{a^{4} - 2 a^{2} b^{2} + b^{4}} = ?

Answered by AST last updated on 22/Nov/23

\sqrt{{(a^{2} + b^{2})}^{2}} + \sqrt{{(a^{2} - b^{2})}^{2}} =∣ a^{2} + b^{2} ∣ + ∣ a^{2} - b^{2} ∣

= a^{2} + b^{2} + (a^{2} - b^{2}) = 2 a^{2}

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