2x - 4(3x + 9) ≥ - 3
2x - 12x - 36 ≥ - 3
- 10x ≥ - 3 + 36
- 10x ≥ 33
x ≤ - 3,3
x ∈ (- ∞ ; - 3,3]
1)ОДЗ
x²-55x+90>0
D=3025-360=2665
x1=(55-√2665)/2 u x2=(55+√2665)/2
+ _ +
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(55-√2665)/2 (55+√2665)/2
x<(55-√2665)/2 U x>(55+√2665)/2
x-36>0⇒x>36
x∈(36;∞)
0,5[lg(x²-55x+90)-lg(x-36)]=0,5lg2
0,5[lg(x²-55x+90)/(x-36)]=0,5lg2
lg(x²-55x+90)/(x-36)=lg2
(x²-55x+90)/(x-36)=2
x²-55x+90-2x+72=0
x²-57x+162=0
x1+x2=57 U x1*x2=162
x1=3∉ОДЗ
x2=54
2)2tg³x-2tg²x+3tgx-3=0
2tg²x(tgx-1)+3(tgx-1)=0
(2tg²x+3)(tgx-1)=0
2tg²x+3>0 при любом х
tgx=1
x=π/4+πn
7х×(x-7)=0
7x=0 или x-7=0
x=0 или х=7
ответ: 0;7
(2x - 5)^2 = 4x^2 - 9
4x^2 - 20x + 25 = 4x^2 - 9
4x^2 - 20x + 25 - 4x^2 + 9 = 0
- 20x + 34 = 0
- 20x = - 34
x = 34/20
x = 1,7