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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality (2^(1-t)-1)/(2^(1-t)+1)+(2^(1-t^2)-1)/(2^(1-t^2)+1) <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( 2 ^ ( 1 - t ) - 1 ) / ( 2 ^ ( 1 - t ) + 1 ) + ( 2 ^ ( 1 - t ^ 2 ) - 1 ) / ( 2 ^ ( 1 - t ^ 2 ) + 1 ) <0 (1)
From the definition field of divisor
2 ^ ( 1 - x ) + 1 ≠ 0 (2 )
From the definition field of divisor
2 ^ ( 1 - x ^ 2 ) + 1 ≠ 0 (3 )
From inequality(1):
-52747253/1000000 < t < -52651807/1000000 或 -52547901/1000000 < t < -13097037/250000 或 -13097037/250000 < t < -2 或 t > 1
From inequality(2):
t ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequality(3):
t ∈ 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)
-52747253/1000000 < t < -52651807/1000000 或 -52547901/1000000 < t < -13097037/250000 或 -13097037/250000 < t < -2 或 t > 1 (4)
From inequalities (3) and (4)
-52747253/1000000 < t < -52651807/1000000 或 -52547901/1000000 < t < -13097037/250000 或 -13097037/250000 < t < -2 或 t > 1 (5)
The final solution set is :
-52747253/1000000 < t < -52651807/1000000 或 -52547901/1000000 < t < -13097037/250000 或 -13097037/250000 < t < -2 或 t > 1Your problem has not been solved here? Please take a look at the hot problems !