(b⁴-b²+1)(b⁴+b²+1)=((b⁴+1)-b²)((b⁴+1)+b²)=(b⁴+1)²-b⁴=b⁸+2b⁴+1-b⁴=b⁸+b⁴+1
3х - у = 3 ⇒ у= -3+3х
5х + 2у = 16 5х+2у=16
5х + 2(-3+3х) = 16
5х - 6 + 6х = 16 у = -3 + 3*2
11х = 22 у=3
х=2
Ответ: (2;3)
3 - (х-2у)-4у=18 ⇒ 3-х+2у-4у=18 ⇒ -х-2у=15 ⇒ х+2у=-15
2х-3у+3=2(3х-у) 2х-3у+3=6х-2у -4х-у=-3 4х+у=3
х+2у=-15
у=3-4х
х+2(3-4х)=-15 у=3-4*3
х+6-8х=-15 у= -9
-7х=-21
-х=3
х=3
Ответ (3; -9)
S₃ = 9 (a₁ + a₁ +2d)*3/2 = 9 а₁ + d = 3 a₁ +d = 3
S₆ = -63 (а₁ + а₁ + 5d)*6/2 = 63, (2a₁ +5d)*3 = 63 2a₁ + 5d = 21
решаем эту систему:
a₁ +d = 3 | *(-2) -2a₁ -2d = -6
2a₁ + 5d = 21 2a₁ + 5d = 21 Cложим, получим: 3d = 15, d = 5
подставим d = 5 в 1-е уравнение: а₁ + 25 =21, а₁ = -4
S₁₀ = (a₁ + a₁ +9d)*10/2 = (2a₁ +9d)*5 =( -8 +45)*5 = 37*5 = 185
2.10 b) a² -ac +bc -ab =a(a -c) -b(a -c) =(a -c)(a -b)
(a+2b)/3(a -b) -(3c -a)/2(a-c) +(a² -bc)/(a -c)(a -b) =
=(2(a-c)(a+2b) -3(a-b)(3c-a) +6(a²-bc)) /6(a-c)(a-b) =
=(2(a²+2ab-ac-2bc) -3(3ac-a² -3bc+ab) +6a² -6bc) /6(a -c)(a -b) =
=(2a²+4ab -2ac-4bc -9ac +3a² +9bc -3ab +6a² -6bc) /6(a -c)(a -b) =
=(11a² +ab -11ac -bc) /6(a -c)(a -b) =
=11a(a -c) +b(a -c)) /6(a -c)(a -b) =
=(a -c)(11a +b) /6(a -c)(a -b) =
=(11a +b) /6(a -b) =(11/6 -1) /6(1/6 +1) =
=(11-6)/6 : 6*7/6 =5/6 : 7 =5/6 *1/7 =5/42
