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2013 Saudi Arabia Pre-TST
1.1
\sqrt{(1- x^2)(1 - y^2) } <=2(1 - x)(1 - y) + 1
\sqrt{(1- x^2)(1 - y^2) } <=2(1 - x)(1 - y) + 1
Source: 2013 Saudi Arabia Pre-TST 1.1
September 13, 2020
algebra
inequalities
Problem Statement
Let
−
1
≤
x
,
y
≤
1
-1 \le x, y \le 1
−
1
≤
x
,
y
≤
1
. Prove the inequality
2
(
1
−
x
2
)
(
1
−
y
2
)
≤
2
(
1
−
x
)
(
1
−
y
)
+
1
2\sqrt{(1- x^2)(1 - y^2) } \le 2(1 - x)(1 - y) + 1
2
(
1
−
x
2
)
(
1
−
y
2
)
≤
2
(
1
−
x
)
(
1
−
y
)
+
1
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