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1.
а) х(х-12)<(х-6)²
Раскрываем скобки:
x²-12x < x²-12x+36
0< 36 - верно
б) х(х+2)>2х-3
Раскрываем скобки:
x²+2x>2x-3
x²+3>0 - верно при любом х
2.
8 < х < 9
а)
Умножаем на 2:
16 < 2x < 18
Вычитаем 3 из всех частей неравенства:
16 - 3 < 2x - 3< 18 - 3
13 < 2x - 3 < 15
б)
Умножаем на (-2), при этом меняем знак неравенства:
- 16> -2x > - 18
Записываем в привычном виде:
-18 < -2x < -16
Прибавляем 5 ко всем частям неравенства:
-18 + 5 < 5 - 2x < - 16 + 5
-13 < 5 -2x < -11
3.
1,4<√2<1,5
1,7<√3<1,8
а)
складываем
1,4 + 1,7 < √2 + √3 < 1,5 + 1,8
3,1 < √2 + √3 < 3,3
б)
√12=√(4·3)=√4·√3=2√3
Умножаем первое неравенство на (-1), при этом меняем знак:
-1,5 < - √2 < -1,4
Умножаем второе неравенство на 2:
1,7·2 < 2·√3 < 2·1,8
-1,5 < - √2 < -1,4
3,4 < 2·√3 < 3,6
Cкладываем
-1,5 + 3,4 < 2√3 - √2 < -1,4+3,6
1,9 < √12 - √2 < 2,2
