Очевидно, так как m, n, k ≥ 1, то
mn ≤ mnk
mk ≤ mnk
nk ≤ mnk
Складываем три неравенства и получаем искомое:
mn + mk + nk ≤ mnk + mnk + mnk = 3mnk
4х^2-5x-6=0
D=121
x1=-0.75
x2=2
-0.75+2=1.25
Ответ В
#2
1)
![( \frac{3 {c}^{4} }{7b {m}^{5} } ) = \frac{9 {c}^{8} }{49 {b}^{2} {m}^{10} }](https://tex.z-dn.net/?f=%28+%5Cfrac%7B3+%7Bc%7D%5E%7B4%7D+%7D%7B7b+%7Bm%7D%5E%7B5%7D+%7D+%29+%3D+%5Cfrac%7B9+%7Bc%7D%5E%7B8%7D+%7D%7B49+%7Bb%7D%5E%7B2%7D+%7Bm%7D%5E%7B10%7D+%7D+)
2)
![\frac{m + n}{m - n} + \frac{m}{n} = \frac{n \times (m + n) + m \times (m - n)}{n \times (m - n)} = \frac{mn + {n}^{2} + {m}^{2} - mn }{mn - {n}^{2} } = \frac{ {n}^{2} + {m}^{2} }{mn - {n}^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7Bm+%2B+n%7D%7Bm+-+n%7D+%2B+%5Cfrac%7Bm%7D%7Bn%7D+%3D+%5Cfrac%7Bn+%5Ctimes+%28m+%2B+n%29+%2B+m+%5Ctimes+%28m+-+n%29%7D%7Bn+%5Ctimes+%28m+-+n%29%7D+%3D+%5Cfrac%7Bmn+%2B+%7Bn%7D%5E%7B2%7D+%2B+%7Bm%7D%5E%7B2%7D+-+mn+%7D%7Bmn+-+%7Bn%7D%5E%7B2%7D+%7D+%3D+%5Cfrac%7B+%7Bn%7D%5E%7B2%7D+%2B+%7Bm%7D%5E%7B2%7D+%7D%7Bmn+-+%7Bn%7D%5E%7B2%7D+%7D+)
3)
![\frac{3 {x}^{2} }{ {x}^{2} - 1} - \frac{3x}{x - 1} = \frac{3 {x}^{2} }{(x - 1)(x + 1)} - \frac{3x}{x - 1} = \frac{3 {x}^{2} - 3x(x + 1) }{(x - 1)(x + 1)} = \frac{3 {x}^{2} - 3 {x}^{2} - 3x }{ {x}^{2}1 } = \frac{ - 3x}{ {x}^{2}1 } = - \frac{3x}{ {x}^{2} - 1}](https://tex.z-dn.net/?f=+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+%7D%7B+%7Bx%7D%5E%7B2%7D+-+1%7D+-+%5Cfrac%7B3x%7D%7Bx+-+1%7D+%3D+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+%7D%7B%28x+-+1%29%28x+%2B+1%29%7D+-+%5Cfrac%7B3x%7D%7Bx+-+1%7D+%3D+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+-+3x%28x+%2B+1%29+%7D%7B%28x+-+1%29%28x+%2B+1%29%7D+%3D+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+-+3+%7Bx%7D%5E%7B2%7D+-+3x+%7D%7B+%7Bx%7D%5E%7B2%7D1+%7D+%3D+%5Cfrac%7B+-+3x%7D%7B+%7Bx%7D%5E%7B2%7D1+%7D+%3D+-+%5Cfrac%7B3x%7D%7B+%7Bx%7D%5E%7B2%7D+-+1%7D+)
4)
![\frac{2 {y}^{2} }{y - 8} - 2y = \frac{2 {y}^{2} - 2y(y - 8)}{y - 8} = \frac{2 {y}^{2} - 2 {y}^{2} + 16y}{y - 8} = \frac{16y}{y - 8}](https://tex.z-dn.net/?f=+%5Cfrac%7B2+%7By%7D%5E%7B2%7D+%7D%7By+-+8%7D+-+2y+%3D+%5Cfrac%7B2+%7By%7D%5E%7B2%7D+-+2y%28y+-+8%29%7D%7By+-+8%7D+%3D+%5Cfrac%7B2+%7By%7D%5E%7B2%7D+-+2+%7By%7D%5E%7B2%7D+%2B+16y%7D%7By+-+8%7D+%3D+%5Cfrac%7B16y%7D%7By+-+8%7D+)
#3
![(3a - {a}^{2} ) ^{2} - {a}^{2} (a - 2)(a + 2) + 2a(7 + 3 {a}^{2} ) = 9 {a}^{2} - 6 {a}^{3} + {a}^{4} - {a}^{2} ( {a}^{2} - 4) + 14a + 16 {a}^{3} = 9 {a}^{2} - 6 {a}^{3} + {a}^{4} - {a}^{4} + 4 {a}^{2} + 14a + 6 {a}^{3} = 13 {a}^{2} + 14a](https://tex.z-dn.net/?f=%283a+-+%7Ba%7D%5E%7B2%7D+%29+%5E%7B2%7D+-+%7Ba%7D%5E%7B2%7D+%28a+-+2%29%28a+%2B+2%29+%2B+2a%287+%2B+3+%7Ba%7D%5E%7B2%7D+%29+%3D+9+%7Ba%7D%5E%7B2%7D+-+6+%7Ba%7D%5E%7B3%7D+%2B+%7Ba%7D%5E%7B4%7D+-+%7Ba%7D%5E%7B2%7D+%28+%7Ba%7D%5E%7B2%7D+-+4%29+%2B+14a+%2B+16+%7Ba%7D%5E%7B3%7D+%3D+9+%7Ba%7D%5E%7B2%7D+-+6+%7Ba%7D%5E%7B3%7D+%2B+%7Ba%7D%5E%7B4%7D+-+%7Ba%7D%5E%7B4%7D+%2B+4+%7Ba%7D%5E%7B2%7D+%2B+14a+%2B+6+%7Ba%7D%5E%7B3%7D+%3D+13+%7Ba%7D%5E%7B2%7D+%2B+14a)
p.s. В последнем примере нужно листать в лево. Пример вышел очень большим.
Система:
x - первое число
y - второе число
y+2 = x
xy=40
Подстановкой (подставим х во второе уравнение):
x=y+2
y^2+2y-40 =0 (1)
(1) y^2+2y-40 = 0
D1 = k^2-ac
D1 = 1+40 = 41
y1 = -1+sqrt(41)
y2 = -1-sqrt(41)
x=y-2
y1 = -1+sqrt (41)
y2 = -1-sqrt (41)
x1 =-3 + sqrt (41)
y1 = -1+sqrt (41)
x2 = -3 - sqrt (41)
y2 = -3 - sqrt (41)
Пусть х-количество 9%-ного сплава
тогда у-количество 30%-ного сплава
300*23%=69 кг цинка будет в 300 кг 23%-ного сплава
9%=0,09
30%=0,3
![\left \{ {{x+y=300} \atop {0.09x+0.3y=69}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%2By%3D300%7D+%5Catop+%7B0.09x%2B0.3y%3D69%7D%7D+%5Cright.+)
х=300-у
0,09(300-у)+0,3у=69
27-0,09у+0,3у=69
0,21у=42
у=42:0,21
у=
200 кг 30%-ного сплава нужно взятьх=300-200=
100 кг 9%-ного сплава нужно взять