ВI.
5х³ - 45х= 5х(х² - 9) = 5х(х² - 3²)=5х(х-3)(х+3)
13х²+26ху +13у² = 13(х² +2ху +у²)=13(х+у)²= 13(х+у)(х+у)
m⁶ - 64 = (m³)² - (2³)² = (m³-2³)(m³ + 2³)=
=(m-2)(m²+2m +2²)(m+2)(m² -2m+2²)= (m-2)(m+2)(m²-2m+4)(m²+2m+4)
7x³-28x=0
7x(x² -4)=0
7x(x-2)(x+2)=0
произведение = 0, если один из множителей = 0
7x=0
x₁=0
x-2=0
x₂=2
x+2=0
x₃=-2
а² - 8а - 33 = а² + 3а - 11а +33 = а(а+3) - 11(а+3) = (а-11)(а+3)
ВII.
12а² - 3b² = 3(4a² - b²) = 3(2a-b)(2a+b)
20c³-20c²+5c = 5c(4c²-4c + 1) = 5c((2c)² - 2*2c*1 + 1²) =
=5c(2c-1)²= 5c(2c-1)(2c-1)
d⁴ - 81 = (d²)² - (3²)² = (d² - 3²)(d² +3²) = (d-3)(d+3)(d² + 9)
x³ + 8x² + 16x = 0
x(x² + 8x + 16) = 0
x(x² + 2*x*4 + 4²) = 0
x(x+4)² = 0
x(x+4)(x+4) = 0
x₁ = 0
x + 4= 0
x₂ = -4
y² + 10y - 75 = y² - 5y + 15y - 75 = y(y-5) + 15(y - 5) =
= (y + 15)(y - 5)
X²-14x+24=0
{x₁x₂=24 x₁=12
{x₁₊x₂=14 x₂=2
по теореме виета
или
D=(-7)²((b/2)²)-24
D=25
x₁,₂=-(b/2)⁺₋√D
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a
x₁,₂=7⁺₋√25
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1
x₁=7+5=12 x₂=7-5=2
по дискриминанту
6х-56-72х=-2х-8
6х-72х+2х=-8+56
-64х=48
х=-0,75
