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Assignment:Find the solution set of inequality [sqrt(x+1)*(2x-1)*(2x-1)*(3x-5)]/(x+2) >x+5 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( sqrt ( x + 1 ) * ( 2 * x - 1 ) * ( 2 * x - 1 ) * ( 3 * x - 5 ) ) / ( x + 2 ) > x + 5 (1)
From the definition field of √
x + 1 ≥ 0 (2 )
From the definition field of divisor
x + 2 ≠ 0 (3 )
From inequality(1):
x > 2.168956
From inequality(2):
x ≥ -1
From inequality(3):
x < -2 或 x > -2
From inequalities (1) and (2)
x > 2.168956 (4)
From inequalities (3) and (4)
x > 2.168956 (5)
The final solution set is :
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