<span>Берем частные поризводные и приравниваем к 0 </span>
<span>z(x, y) = (5x - 4y + 3)^2 + (3x - y - 1)^2 </span>
<span>dz/dx = 2(5x - 4y + 3)*5 + 2(3x - y - 1)*3 = 10(5x - 4y + 3) + 6(3x - y - 1) = 0 </span>
<span>dz/dy = 2(5x - 4y + 3)*(-4) + 2(3x - y - 1)*(-1) = -8(5x - 4y + 3) - 2(3x - y - 1) = 0 </span>
<span>Решаем систему </span>
<span>{ 50x - 40y + 30 + 18x - 6y - 6 = 0 </span>
<span>{ -40x + 32y - 24 - 6x + 2y + 2 = 0 </span>
<span>Приводим подобные и сокращаем на 2 </span>
<span>{ 34x - 23y + 12 = 0 </span>
<span>{ -23x + 17y - 11 = 0 </span>
<span>Умножаем 1 ур на 17, а 2 на 23 </span>
<span>{ 578x -23*17y + 204 = 0 </span>
<span>{ -529x + 23*17y - 253 = 0 </span>
<span>Складываем уравнения </span>
<span>49x - 49 = 0, x = 1 </span>
<span>23y = 34 + 12 = 46, y = 2 </span>
<span>Точка минимума: x = 1, y = 2 </span>
<span>z(1, 2) = (5 - 8 + 3)^2 + (3 - 2 - 1)^2 = 0 + 0 = 0</span>
1) (x-2)²-(x-1)(x+2)=x²-4x+4-x²-2x+x+2=-6x+6=6(1-x)
2)5x+5y=12
x-2y=-7, x=-7+2y
5(-7+2y)+5y=12
-35+10y+5y=12
15y=47
y=47/15
x=-7+2*47/15=-105+94/15=-11/15
(-11/15;47/15)
а) 7х/12у = 2х*7х/24ху = 14х^2/24ху
5у/8х= 3у*5у/24ху = 15у^2/24ху
б) 3b/а = (а+b)*3b/а(а+b) = 3аb-3b^2/a^2+ab
а/а+b = а^2/а(а+b) = a^2/a^2+ab
в) m/m+n = (m-n)*m/(m+n)(m-n) = m^2-mn/m^2-n^2
n/m-n = (m+n)*n/(m+n)(m-n) = mn+n^2/m^2-n^2
г) 2а/3а-3 = 2а/3(а-1) = 2а(а+1)/3(a-1)(a+1) = 2a^2+2a/3a^2-3
а+2/а^2-1 = а+2/(а-1)(а+1) = 3(а+2)/3(a-1)(a+1) = 3a+6/3a^2-3