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2014 Saudi Arabia Pre-TST
4.2
(x^2 + 1)^6 /2^7 +1/2 x^5 - x^3 + x for x>=0
(x^2 + 1)^6 /2^7 +1/2 x^5 - x^3 + x for x>=0
Source: 2014 Saudi Arabia Pre-TST 4.2
September 13, 2020
algebra
inequalities
Problem Statement
Given
x
≥
0
x \ge 0
x
≥
0
, prove that
(
x
2
+
1
)
6
2
7
+
1
2
≥
x
5
−
x
3
+
x
\frac{(x^2 + 1)^6}{2^7}+\frac12 \ge x^5 - x^3 + x
2
7
(
x
2
+
1
)
6
+
2
1
≥
x
5
−
x
3
+
x
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