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580
ASU 580 Commonwealth of Independent States 1991 (a-d)^2>=4d+8 if ad=bc
ASU 580 Commonwealth of Independent States 1991 (a-d)^2>=4d+8 if ad=bc
Source:
August 15, 2019
algebra
inequalities
diophantine
Problem Statement
If
a
>
b
>
c
>
d
>
0
a > b > c > d > 0
a
>
b
>
c
>
d
>
0
are integers such that
a
d
=
b
c
ad = bc
a
d
=
b
c
, show that
(
a
−
d
)
2
≥
4
d
+
8
(a - d)^2 \ge 4d + 8
(
a
−
d
)
2
≥
4
d
+
8
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