ОДЗ: a² -7a+10≠0
a² -7a+10=0
D=49-40=9
a₁=(7-3)/2=2
a₂=(7+3)/2=5
a≠2 и a≠5
[2(11-5a)-3(a²-7a+10)]/[2(a²-7a+10)]≥0
[22-10a-3a²+21a-30]/[2(a²-7a+10)]≥0
[-3a²+11a-8]/[2(a²-7a+10)]≥0
-[3a²-11a+8]/[2(a²-7a+10)]≥0
[3a²-11a+8]/[2(a²-7a+10)]≤0
Раскладываем на множители:
1) a²-7a+10=(a-2)(a-5)
2) 3a²-11a+8=0
D=121-96=25
a₁=(11-5)/6=1
a₂=(11+5)/6=16/6=8/3=2 ²/₃
3a²-11a+8=3(a-1)(a-2 ²/₃)
[3(a-1)(a-2 ²/₃)]/[2(a-2)(a-5)]≤0
(a-1)(a-2 ²/₃)(a-2)(a-5)≤0
a=1 a=2 ²/₃ a=2 a=5
+ - + - +
--------- 1 ----------- 2 ----------- 2 ²/₃ ------------ 5 ------------
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a∈(1; 2)U(2 ²/₃; 5)