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Assignment:Find the solution set of inequality -2000+(500/(1+r))+(700/(1+r)^2)+(2000/(1+r)^2) >-10000+(8000/(1+r))+(2500/(1+r)^2)+(2000/(1+r)^2) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
-2000 + ( 500 / ( 1 + r ) ) + ( 700 / ( 1 + r ) ^ 2 ) + ( 2000 / ( 1 + r ) ^ 2 ) > -10000 + ( 8000 / ( 1 + r ) ) + ( 2500 / ( 1 + r ) ^ 2 ) + ( 2000 / ( 1 + r ) ^ 2 ) (1)
From the definition field of divisor
1 + x ≠ 0 (2 )
From the definition field of divisor
1 + x ≠ 0 (3 )
From the definition field of divisor
1 + x ≠ 0 (4 )
-10000 + ( 8000 / ( 1 + r ) ) + ( 2500 / ( 1 + r ) ^ 2 ) + ( 2000 / ( 1 + r ) ^ 2 ) >0 (5)
From the definition field of divisor
1 + x ≠ 0 (6 )
From the definition field of divisor
1 + x ≠ 0 (7 )
From the definition field of divisor
1 + x ≠ 0 (8 )
From inequality(1):
r < -1.198128 或 r > 0.135628
From inequality(2):
r < -1 或 r > -1
From inequality(3):
r < -1 或 r > -1
From inequality(4):
r < -1 或 r > -1
From inequality(5):
-1.381025 < r < 0.181025
From inequality(6):
r < -1 或 r > -1
From inequality(7):
r < -1 或 r > -1
From inequality(8):
r < -1 或 r > -1
From inequalities (1) and (2)
r < -1.198128 或 r > 0.135628 (9)
From inequalities (3) and (9)
r < -1.198128 或 r > 0.135628 (10)
From inequalities (4) and (10)
r < -1.198128 或 r > 0.135628 (11)
From inequalities (5) and (11)
-1.381025 < r < -1.198128 或 0.135628 < r < 0.181025 (12)
From inequalities (6) and (12)
-1.381025 < r < -1.198128 或 0.135628 < r < 0.181025 (13)
From inequalities (7) and (13)
-1.381025 < r < -1.198128 或 0.135628 < r < 0.181025 (14)
From inequalities (8) and (14)
-1.381025 < r < -1.198128 或 0.135628 < r < 0.181025 (15)
The final solution set is :
-1.381025 < r < -1.198128 或 0.135628 < r < 0.181025 Your problem has not been solved here? Please take a look at the hot problems !