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History of Inequality Computation > Answer
Overview: 2 questions will be solved this time.Among them
☆2 inequalities
[ 1/2Inequality]
Assignment:Find the solution set of inequality 0 <(a+13-sqrt((a+13)*(a+13)-28(a*a-a-2)))/2 <1 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
0 < ( a + 13 - sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2 (1)
( a + 13 - sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2 <1 (2)
From the definition field of √
( x + 13 ) * ( x + 13 ) - 28 * ( x * x - x - 2 ) ≥ 0 (3 )
From inequality(1):
a < -1 或 a > 2
From inequality(2):
-1.43875 < a < 2.581607
From inequality(3):
-2.05505 ≤ a ≤ 4.05505
From inequalities (1) and (2)
-1.43875 < a < -1 或 2 < a < 2.581607 (4)
From inequalities (3) and (4)
-1.43875 < a < -1 或 2 < a < 2.581607 (5)
The final solution set is :
-1.43875 < a < -1 或 2 < a < 2.581607 [ 2/2Inequality]
Assignment:Find the solution set of inequality 1 <(a+13+sqrt((a+13)*(a+13)-28(a*a-a-2)))/2 <2 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
1 < ( a + 13 + sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2 (1)
( a + 13 + sqrt ( ( a + 13 ) * ( a + 13 ) - 28 * ( a * a - a - 2 ) ) ) / 2 <2 (2)
From the definition field of √
( x + 13 ) * ( x + 13 ) - 28 * ( x * x - x - 2 ) ≥ 0 (3 )
From inequality(1):
a > -2.10848
From inequality(2):
a < -2.096613
From inequality(3):
-2.05505 ≤ a ≤ 4.05505
From inequalities (1) and (2)
-2.10848 < a < -2.096613 (4)
From inequalities (3) and (4)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (5)
The final solution set is :
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!Your problem has not been solved here? Please take a look at the hot problems !