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10 cards from this deck
Prove that the expression is greater than or equal to zero.
It is always greater than or equal to zero, i.e., x2≥0x^2 \geq 0x2≥0 for any real number xxx.
a2+b2≥2aba^2 + b^2 \geq 2aba2+b2≥2ab.
Rewrite the inequality to isolate variables if possible.
(a−b)2≥0(a-b)^2 \geq 0(a−b)2≥0.
Show x2−x+1>0x^2 - x + 1 > 0x2−x+1>0.
It's expressed as (x−1/2)2+3/4>0(x-1/2)^2 + 3/4 > 0(x−1/2)2+3/4>0.
The squared term is positive and 3/43/43/4 is also positive.
Using the method of AM-GM inequality.
It simplifies the expression and reveals positivity.
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