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☆1 inequalities
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Assignment:Find the solution set of inequality (9+4x-3x∧2+√(9×x×x×x×x-96×x×x×x+346×x×x-600x+441))÷4÷(x-1) >3÷2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( 9 + 4 * x - 3 * x ^ 2 + √ ( 9 × x × x × x × x - 96 × x × x × x + 346 × x × x - 600 * x + 441 ) ) ÷ 4 ÷ ( x - 1 ) >3 ÷ 2 (1)
From the definition field of √
9 × x × x × x × x - 96 × x × x × x + 346 × x × x - 600 * x + 441 ≥ 0 (2 )
From inequality(1):
1 < x < 2
From inequality(2):
x ≤ 2.012472 或 x ≥ 5.723438
From inequalities (1) and (2)
1 < x < 2 (3)
The final solution set is :
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