If-a-lt-b-lt-0-then-a-b-a-b-ab-

Question Number 182947 by myint last updated on 17/Dec/22

If a < b < 0, then ∣ a - b ∣ + ∣ a + b ∣ + ∣ ab ∣=

Commented by mr W last updated on 17/Dec/22

\neq c o n s t a n t v a l u e!

c o u l d b e a n y p o s i t i v e v a l u e!

Answered by Frix last updated on 17/Dec/22

a < b < 0 \Rightarrow a - b < 0 \land a + b < 0 \land a b > 0 \Rightarrow

∣ a - b ∣ + ∣ a + b ∣ + ∣ a b ∣=

= - (a - b) - (a + b) + a b =

= - 2 a + a b = a (b - 2)

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