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Assignment:Find the solution set of inequality x^2-x-2
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
x ^ 2 - x - 2 < log( 2 , x + 2 ) - log( sqrt ( 2 ) , x ) (1)
From the definition field of log
2 > 0 (2 )
x + 2 > 0 并且 ≠ 1 (3 )
From the definition field of log
sqrt ( 2 ) > 0 (4 )
x > 0 并且 ≠ 1 (5 )
From inequality(1):
x < 2
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):
-2 < x < -1 或 x > -1
From inequality(4):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(5):
0 < x < 1 或 x > 1
From inequalities (1) and (2)
x < 2 (6)
From inequalities (3) and (6)
-2 < x < -1 或 -1 < x < 2 (7)
From inequalities (4) and (7)
-2 < x < -1 或 -1 < x < 2 (8)
From inequalities (5) and (8)
x > 或 0 < x < 1 或 1 < x < 2 (9)
The final solution set is :
x > 或 0 < x < 1 或 1 < x < 2 Your problem has not been solved here? Please take a look at the hot problems !