If (x^2-5x+4)(y^2+y+1)<2y for all real y, then x belongs to

coraletsmmh

coraletsmmh

Answered question

2022-04-21

If (x25x+4)(y2+y+1)<2y for all real y, then x belongs to the interval (2,b), then b can be?

Answer & Explanation

Payton Cantrell

Payton Cantrell

Beginner2022-04-22Added 15 answers

From y2+y+1=(y+12)2+34>0,
we know that we may divide by y2+y+1. What can we say about 2yy2+y+1? For y0, this will be positive, but what about negative y? We have
y2+y+1=(y1)2yy
with equality y=1. Therefore, 2yy2+y+12
with equality y=1. So what you really want is
x25x+4<2.

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