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Assignment:Find the solution set of inequality ln(2x+2(4x*x+1)^(-0.5)+((2x+2(4x*x+1)^(-0.5))^2+1)^0.5)+2(x+(4x*x+1)^(-0.5))*(4*(x+(4x*x+1)^(-0.5))^2+1)^0.5-5.9 ≤5.2*((50-x*x+(4x*x+1)^-1)^2-x*x)^0.5 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln ( 2 * x + 2 * ( 4 * x * x + 1 ) ^ ( -0.5 ) + ( ( 2 * x + 2 * ( 4 * x * x + 1 ) ^ ( -0.5 ) ) ^ 2 + 1 ) ^ 0.5 ) + 2 * ( x + ( 4 * x * x + 1 ) ^ ( -0.5 ) ) * ( 4 * ( x + ( 4 * x * x + 1 ) ^ ( -0.5 ) ) ^ 2 + 1 ) ^ 0.5 - 5.9 ≤5.2 * ( ( 50 - x * x + ( 4 * x * x + 1 ) ^ -1 ) ^ 2 - x * x ) ^ 0.5 (1)
From the definition field of ln
2 * x + 2 * ( 4 * x * x + 1 ) ^ ( -0.5 ) + ( ( 2 * x + 2 * ( 4 * x * x + 1 ) ^ ( -0.5 ) ) ^ 2 + 1 ) ^ 0.5 > 0 (2 )
From inequality(1):
x ≤ 6.52341 或 x ≥ 7.664022
From inequality(2):
x > -0.961404
From inequalities (1) and (2)
-0.961404 < x ≤ 6.52341 或 x ≥ 7.664022 (3)
The final solution set is :
-0.961404 < x ≤ 6.52341 或 x ≥ 7.664022Your problem has not been solved here? Please take a look at the hot problems !