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Assignment:Find the solution set of inequality (x^2+2)/(sqrt(x^2+1)) >= 2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( x ^ 2 + 2 ) / ( sqrt ( x ^ 2 + 1 ) ) >= 2 (1)
From the definition field of √
x ^ 2 + 1 ≥ 0 (2 )
From the definition field of divisor
sqrt ( x ^ 2 + 1 ) ≠ 0 (3 )
From inequality(1):
x ≤ 87/500000 或 87/500000 ≤ x ≤ 87/500000 或 x ≥ 87/500000
From inequality(2):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
x ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequalities (1) and (2)
x ≤ 87/500000 或 87/500000 ≤ x ≤ 87/500000 或 x ≥ 87/500000 (4)
From inequalities (3) and (4)
x ≤ 87/500000 或 87/500000 ≤ x ≤ 87/500000 或 x ≥ 87/500000 (5)
The final solution set is :
x ≤ 87/500000 或 87/500000 ≤ x ≤ 87/500000 或 x ≥ 87/500000Your problem has not been solved here? Please take a look at the hot problems !