current location:Mathematical operation >
History of Inequality Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality -(128*(14*t-6))/((7*t^2-1)*(7*t^2-6*t+1)^2)-(1792*t)/((7*t^2-1)^2*(7*t^2-6*t+1)) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
-( 128 * ( 14 * t - 6 ) ) / ( ( 7 * t ^ 2 - 1 ) * ( 7 * t ^ 2 - 6 * t + 1 ) ^ 2 ) - ( 1792 * t ) / ( ( 7 * t ^ 2 - 1 ) ^ 2 * ( 7 * t ^ 2 - 6 * t + 1 ) ) >0 (1)
From the definition field of divisor
( 7 * x ^ 2 - 1 ) * ( 7 * x ^ 2 - 6 * x + 1 ) ^ 2 ≠ 0 (2 )
From the definition field of divisor
( 7 * x ^ 2 - 1 ) ^ 2 * ( 7 * x ^ 2 - 6 * x + 1 ) ≠ 0 (3 )
From inequality(1):
t < -0.191541 或 0.297893 < t < 0.536504
From inequality(2):
t < -1/√7 或 -1/√7 < t < 226541/1000000 或 226541/1000000 < t < 1/√7 或 1/√7 < t < 315301/500000 或 t > 315301/500000
From inequality(3):
t < -75593/200000 或 -75593/200000 < t < 0.226541 或 0.226541 < t < 94491/250000 或 94491/250000 < t < 0.630602 或 t > 0.630602
From inequalities (1) and (2)
t < -1/√7 或 -1/√7 < t < -0.191541 或 t < -1/√7 或 或 0.297893 < t < 1/√7 或 1/√7 < t < 0.536504 (4)
From inequalities (3) and (4)
t < -75593/200000 或 -75593/200000 < t < -1/√7 或 -1/√7 < t < -0.191541 或 -75593/200000 < t < -1/√7 或 0.297893 < t < 94491/250000 或 94491/250000 < t < 1/√7 或 1/√7 < t < 0.536504 (5)
The final solution set is :
t < -75593/200000 或 -75593/200000 < t < -1/√7 或 -1/√7 < t < -0.191541 或 -75593/200000 < t < -1/√7 或 0.297893 < t < 94491/250000 或 94491/250000 < t < 1/√7 或 1/√7 < t < 0.536504 Your problem has not been solved here? Please take a look at the hot problems !