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# I really need help on this...

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Apr 23, 2022

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We use a geometric approach because we see that if a and b are side lengths of a triangle and the included angle is 60 degrees, then the remaining side is $$\sqrt{a^2 - ab + b^2}$$. Also, if the included angle is 120 degrees instead, then the remaining side is $$\sqrt{a^2 + ab + b^2}$$.

(Please try to prove this using Law of Cosines.)

Refer to the following diagram:

Using triangle inequality on $$\triangle BCD$$ yields the required inequalities immediately.

Exercise: Try to figure out the case when equality holds.

Apr 23, 2022
edited by MaxWong  Apr 23, 2022