GREhelp wrote:
\(s^2 + t^2 < 1-2st\)
Quantity A |
Quantity B |
1 - s |
t |
First notice that we have a perfect square, (s + t)², "hiding" in the given inequality. The perfect square is in the form s² + 2st + t²
Here's what I mean:
Given: s² + t² < 1 - 2st
Add 2st to both sides to get: s² + 2st + t² < 1
Factor the left side: (s + t)² < 1
IMPORTANT:
If (something)² < 1, then it must be the case that
-1 < something < 1Since we now know that (s + t)² < 1, we can say that
-1 < s + t < 1Given:
Quantity A: 1 - s
Quantity B: t
Add s to both sides to get:
Quantity A: 1
Quantity B: s + t
Since
-1 < s + t < 1, we can conclude that Quantity A is greater.
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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