4^х - 9 • 2^х + 8 = 0
2^2х - 9 • 2^х + 8 = 0
2^х = а ; а > 0
а^2 - 9а + 8 = 0
D = 81 - 32 = 49 = 7^2
a1 = ( 9 + 7 ) : 2 = 8
a2 = ( 9 - 7 ) : 2 = 1
1) 2 ^ x = 8
2 ^ X = 2 ^ 3
X = 3
2) 2 ^ x = 1
2 ^ X = 2 ^ 0
X = 0
Ответ 3 ; 0
A^2 - 3ab + 3a - 9b = (a^2 + 3a) - (3ab - 9b) = a(a+ 3) - 3b(a+ 3) = (a+3)(a-3b)
28.
a) (n⁵ + 11n⁴) · m – (n⁵ + 11n⁴)(m – 1)
Открываем скобки:
mn⁵ + 11mn⁴ – mn⁵ + 11mn⁴ – n⁵ – 11n⁴ = 22mn⁴ – n⁵ – 11n⁴ = 11mn⁴ – n⁵.
б) (x + 13)(11 – x) – (x – 6)(x + 2)
Так же открываем скобки:
11x + 143 – x² – 13x = –x² – 2x + 143 = x² + 2x – 143
Дискриминант:
x² + 2x – 143 = 0
D = 2² – 4 · (–143) = 4 + 572 = 576 = 24²
x₁ = = = 11;
x₂ = = = –13.
ax² + bx + c = a(x – x₁)(x – x₂)
x² + 2x – 143 = (x – 11)(x + 13).
29.
а) 3y – 6 – y² + 2y = 0
–y² + 5y – 6 = 0
y² – 5y + 6 = 0
D = (–5)² – 4 · 6 = 25 – 24 = 1
x₁ = = 3;
x₂ = = 2.
б) (2x – 3)(1 – 3x) = (2 – 6x)(x – 8)
Открываем скобки:
2x – 6x² + 3 + 9x = 2x – 16 – 6x² + 48x
6x² – 6x² + 11x – 48x – 2x = –3 – 16
–39x = –19
39x = 19
x = .
Vконуса=(1/3)*Sосн*Н, Sосн =πR², V=(1/3)πR²H
V₁=(1/3)*π*9² *2= 54π
V₂=(1/3)*π*3² *3=9π
V₁/V₂=(54π)/(9π)=6
ответ: в 6 раз