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总述:本次共解1题。其中
☆不等式1题
〖 1/1不等式〗
作业:求不等式 [sqrt(x+1)*(2x-1)*(2x-1)*(3x-5)]/(x+2) >x+5 的解集.
题型:不等式
解:
该不等式可以化为1个不等式:
( sqrt ( x + 1 ) * ( 2 * x - 1 ) * ( 2 * x - 1 ) * ( 3 * x - 5 ) ) / ( x + 2 ) > x + 5 (1)
由√的定义域得
x + 1 ≥ 0 (2 )
由除数的定义域得
x + 2 ≠ 0 (3 )
由不等式(1)得:
x > 2.168956
由不等式(2)得:
x ≥ -1
由不等式(3)得:
x < -2 或 x > -2
由不等式(1)和(2)得
x > 2.168956 (4)
由不等式(3)和(4)得
x > 2.168956 (5)
最终答案为:
x > 2.168956
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