2). а). 3,4a⁻⁸b¹⁰ * 5a⁵b⁻⁹ = 17a⁵⁻⁸b¹⁰⁻⁹ = 17a⁻³b = 17b/a³
b). (5x⁻⁴/2y⁻⁵)⁻² * 100x⁻⁵y⁶ = (2y⁻⁵/5x⁻⁴)² * 100x⁻⁵y⁶ =
= 4y⁻¹⁰/25x⁻⁸ * 100x⁻⁵y⁶ = 16x⁸/y¹⁰ * x⁻⁵y⁶ = 16x³y⁻⁴ = 16x³/y⁴
3). 4200 = 4,2*10³
0,0035 = 3,5*10⁻³
51,1*10⁻² = 5,11*10⁻¹
0,24*10⁵ = 2,4*10⁴
Вариант 2.
1. cos8α cos2α - sin8α sin2α = cos(8α+2α)=cos10α
2. log₆ 81x=4
ОДЗ: х>0
81x=6⁴
3⁴ * x=6⁴
x=6⁴/3⁴
x=(6/3)⁴
x=2⁴
x=16
Ответ: 16
3. f(x)=2x²-16x+3 [-1; 1]
f(x)' = 4x-16
4x-16=0
4x=16
x=4 ∉[-1; 1]
При х=-1 f(-1)=2*(-1)²-16*(-1)+3=2+16+3=21
При х=1 f(1) = 2*1²-16*1+3=2-16+3=-11 - наименьшее значение
Ответ: -11
Вариант 3.
2. cos4x = √2/2
4x= <u>+</u> π/4 + 2πn, n∈Z
x=<u> +</u> π/16 + πn/2, n∈Z
3. f(x)=3x²+7x+5
f(x)' = 6x+7
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