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Assignment:Find the solution set of inequality (x^6+x^5-45)/(√(9+x^2)) >√(x^-5)+7 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( x ^ 6 + x ^ 5 - 45 ) / ( √ ( 9 + x ^ 2 ) ) > √ ( x ^ -5 ) + 7 (1)
From the definition field of √
9 + x ^ 2 ≥ 0 (2 )
From the definition field of divisor
√ ( 9 + x ^ 2 ) ≠ 0 (3 )
From the definition field of √
x ^ -5 ≥ 0 (4 )
From inequality(1):
x < 0 或 x > 1.894094
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 inequality(4):
x ≥ 0
From inequalities (1) and (2)
x < 0 或 x > 1.894094 (5)
From inequalities (3) and (5)
x < 0 或 x > 1.894094 (6)
From inequalities (4) and (6)
x > 1.894094 (7)
The final solution set is :
x > 1.894094Your problem has not been solved here? Please take a look at the hot problems !