Find all values of a that satisfy the

tambustqaze

tambustqaze

Answered question

2022-04-02

Find all values of a that satisfy the inequality for all (x,y).

Answer & Explanation

Brennan Thompson

Brennan Thompson

Beginner2022-04-03Added 10 answers

I need to determine all possible values for a[0,2] such that the following holds for all (x,y)R2:
(2x+ay)(x+6y)+(2y+ax)(20y)0
or equivalent 2x240y221axy+12xy+a6y20
I've plotted the function and observed that it holds for all a[0,α] for some α between 1.3 and 1.4 and it doesn't hold for greater values. But I don't know how to prove it nor find such α.

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