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г)
b₁ + b₂ + b₃ = 7
b₁b₂b₃ = 8
bₙ = b₁ qⁿ⁻¹
b₁ * b₁q * b₁q² = b₁³ q³ = 8
b₁q = 2
b₁ + b₁q + b₁q² = b₁ + b₁q + b₁q*q = b₁ + 2 + 2q = 7
b₁ + 2q = 5
b₁ = 5 - 2q
(5 - 2q)q = 2
2q² - 5q + 2 = 0
D = 25 - 16 = 9
q₁₂ = (5 +- 3)/4 = 2 и 1/2
1. q = 2 b₁ = 5 - 2q = 5 - 4 = 1
2. q = 1/2 b₁ = 5 - 1 = 4
б)
b₂ = 10
b₃ + b₄ = 60
b₃ = b₂q
b₄ = b₃q = b₂q*q = b₂q²
b₂q + b₂q² = 10(q + q²) = 60
q² + q - 6 = 0
D = 1 + 24 = 25
q₁₂ = (-1 +- 5)/2 = 2 и -3
1. q = 2 b₂ = b₁q = 2b₁ = 10 b₁ = 5
2. q=-3 b₂ = b₁q = -3b₁ = 10 b₁ = - 10/3
Преобразование в многочлен
1
3(a+5b)/[0,2(a-5b)(a+5b)]=15/(a-5b)
a-5b=0,4 15:0,4=37,5
2
7(a-2b)/[0,125(a-2b)(a+2b)]=56/(a+2b)
a+2b=14 56:14=4
3
[2x(x²-3)+3y(x²-3)]/[2y(x²6)]=(x²-3)(2x+3y)/[2y(x²-6)]
x/y=1/2⇒y=2x
(x²-3)*(2x+6x)/[4x(x²-6)]=2(x²-3)/(x²-6)
4
[3x(2y²+5)-y(2y²+5)]/[2x(2y²+5)]=(2y²+5)(3x-y)/[2x(2y²+5)]=(3x-y)/2x
x/y=1/7⇒y=7x (3x-7x)/2x=-4x/2x=-2
Найдя дискриминант D=121
x1=3; x2=-2.5;
(x-3)(x+2.5)>0