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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality sqrt(x^2-3*x+1)+sqrt(2*x^2+2x*-5)
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( x ^ 2 - 3 * x + 1 ) + sqrt ( 2 * x ^ 2 + 2 * x * -5 ) < sqrt ( 3 * x ^ 2 + 7 * x - 11 ) + sqrt ( 7 - 8 * x ) (1)
From the definition field of √
x ^ 2 - 3 * x + 1 ≥ 0 (2 )
From the definition field of √
2 * x ^ 2 + 2 * x * -5 ≥ 0 (3 )
From the definition field of √
3 * x ^ 2 + 7 * x - 11 ≥ 0 (4 )
From the definition field of √
7 - 8 * x ≥ 0 (5 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
x ≤ 0.381966 或 x ≥ 2.618034
From inequality(3):
x ≤ 0 或 x ≥ 5
From inequality(4):
x ≤ -3.408937 或 x ≥ 1.075604
From inequality(5):
x ≤ 7/8
From inequalities (1) and (2)
x ≤ 0.381966 或 x ≥ 2.618034 (6)
From inequalities (3) and (6)
x ≤ 0 或 x ≥ 5 (7)
From inequalities (4) and (7)
x ≤ -3.408937 或 x ≥ 5 (8)
From inequalities (5) and (8)
x ≤ -3.408937 (9)
The final solution set is :
x ≤ -3.408937Your problem has not been solved here? Please take a look at the hot problems !