-5x₁ + 3x₂ - x₃ = -5 -5 3 -1 -5 D = -5*3*5 + 3*(-3)*2 + (-1)*2*1 -
-5x₁ + 3x₂ - 3x₃ = -1 -5 3 -3 -1 - 3*(-5)*5 - (-5)*(-3)*(-1) - (-1)*3*2 = 2x₁ - x₂ + 5x₃ = 0 2 -1 5 0 = -75 - 18 - 5 + 75 + 15 + 6 = -2.
-5 3 -1| -5 3 D1 = -75 + 0 - 1 + 15 + 15 - 0 = -46.
-1 3 -3| -1 3
0 -1 5| 0 -1
-5 -5 -1| -5 -5 D2 = 25 + 30 + 0 - 125 - 0 - 2 = -72.
-5 -1 -3| -5 -1
2 0 5| 2 0
-5 3 -5| -5 3 D3 = 0 - 6 - 25 - 0 + 5 + 30 = 4.
-5 3 -1| -5 3
2 -1 0| 2 -1
ответ: х1 = -46/-2 = 23,
х2 = -72/-2 = 36,
х3 = 4/-2 = -2.
Проверка.
-5*23+3*36-1*(-2) = -5
-5*23+3*36-3*(-2) = -1
2*23-1*36+5*(-2) = 0
№1
(1-а)²= 1-2a+a²
(3+2у)²= 9+12y+4y²
(4х-5у)²= 16x²-40xy+25y²
№2
у²-49= y²-7² = (y-7)(y+7)
(5х-1)²-16х²= (5x-1)² - (4x)² = (5x-1-4x)(5x-1+4x) = (x-1)(9x-1)
9х²+30ху+25у²= (3х)²+2·3x·5y+(5у)²= (3x+5y)²
№3
(2-а²)(2+а²)= 2²-(a²)² = 4-a⁴
(e-3)(e+3)(e²+9)= (e²-3²)(e²+9) = (e²-9)(e²+9) = e⁴-81
№4
8,7²-1,3²= (8,7-1,3)·(8,7+1,3) = 7,4·10=74
107²-2+4·67+67²= не поняла условие
№5
(2x-1)(2x+1)-2(x-3)²=x(2x-3)
(2x)²-1²-2·(x²-6x+9)=2x²-3x
4x²-1 - 2x²+12x-18=2x²-3x
2x²+12x-19=2x²-3x
2x²+12x-19 - 2x²+3x = 0
15x=19
x=19:15
x=1 ⁴/₁₅
x+4x+4x:2=168
5x+2x=168
7x=168:7
x=24(к)-1,коробка
24*4=96(к)-2 коробка
96:2=48(к)