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Assignment:Find the solution set of inequality x(8√(1-x)+√(1+x)) ≤11√(1+x)-16√(1-x) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
x * ( 8 * √ ( 1 - x ) + √ ( 1 + x ) ) ≤11 * √ ( 1 + x ) - 16 * √ ( 1 - x ) (1)
From the definition field of √
1 - x ≥ 0 (2 )
From the definition field of √
1 + x ≥ 0 (3 )
From the definition field of √
1 + x ≥ 0 (4 )
From the definition field of √
1 - x ≥ 0 (5 )
From inequality(1):
x ≥ 3/5
From inequality(2):
x ≤ 1
From inequality(3):
x ≥ -1
From inequality(4):
x ≥ -1
From inequality(5):
x ≤ 1
From inequalities (1) and (2)
3/5 ≤ x ≤ 1 (6)
From inequalities (3) and (6)
3/5 ≤ x ≤ 1 (7)
From inequalities (4) and (7)
3/5 ≤ x ≤ 1 (8)
From inequalities (5) and (8)
3/5 ≤ x ≤ 1 (9)
The final solution set is :
3/5 ≤ x ≤ 1Your problem has not been solved here? Please take a look at the hot problems !