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2021 Science ON
2021 Science ON grade IX
3
Understanding the condition
Understanding the condition
Source: Science ON 2021 grade IX/3
March 8, 2021
Inequality
algebra
identities
Problem Statement
Real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
with
0
≤
a
,
b
,
c
≤
1
0\le a,b,c\le 1
0
≤
a
,
b
,
c
≤
1
satisfy the condition
a
+
b
+
c
=
1
+
2
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
.
a+b+c=1+\sqrt{2(1-a)(1-b)(1-c)}.
a
+
b
+
c
=
1
+
2
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
.
Prove that
1
−
a
2
+
1
−
b
2
+
1
−
c
2
≤
3
3
2
.
\sqrt{1-a^2}+\sqrt{1-b^2}+\sqrt{1-c^2}\le \frac{3\sqrt 3}{2}.
1
−
a
2
+
1
−
b
2
+
1
−
c
2
≤
2
3
3
.
(Nora Gavrea)
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