3²⁰¹⁶+2*3²⁰¹⁶=3⁴ⁿ⁻³
3*3²⁰¹⁶=3⁴ⁿ⁻³
3²⁰¹⁶⁺¹=3⁴ⁿ⁻³
3²⁰¹⁷=3⁴ⁿ⁻³
2017=4n-3
4n=2020
n=505.
Ответ: n=505.
1.
a) (x-3)*(x-7)-2x*(3x-5)=x²-10x+21-6x²+10x=21-5x².
б) 2*(m+1)²-4m=2(m²+2m+1)-4m=2m²+4m+2-4m=2m²+2=2*(m+1).
в) 4a*(a-2)-(a-4)²=4a²-8a-(a²-8a+16)=4a²-8a-a²+8a-16=3a²-16.
2.
a) x³-9x=x*(x²-9)=x*(x²-3²)=x*(x-3)*(x+3).
б) -5a²-10ab-5b²=-5*(a²+2ab+b²)=-5*(a+b)².
3)
(y²-2y)²-y²*(y+3)*(y-3)+2y*(2y²+5)=y⁴-4y³+4y²-y²*(y²-9)+4y³+10y=
=y⁴-4y³+4y²-y⁴+9y²+4x³+10y=13y²+10y=y*(13y+10).
4.
a) 16x⁴-81=(2x)⁴-3⁴=((2x)²-9)*((2x)²+9)=(2x-3)*(2x+3)*(4x²+9)
б) x²-x-y²-y=(x²-y²)-x-y=(x+y)*(x-y)-(x+y)=(x+y)*(x-y-1).
<span>260 грудусов=4,538 радиана</span>
x^2-y=3 x=3-y x=3-y x=3-y [x= √3
x+y=3 (3-y)^2-y=3 9-6y+y^2-3=0 y^2-6y+6=0 { [ y=3- √3
[x=- √3
[y=3+ √3
y^2-6y+6=0
<span>D</span><span> = b</span>2<span> - 4ac = (-6)</span>2<span> - 4∙1∙6 = 12</span>
<span>D</span><span> > 0 ⇒ уравнение имеет 2 корня</span>
<span>y = -b ± √D / 2a</span>
<span>y1</span><span> = (6 - √12) / (2∙1) = 3- √3</span>
<span>y2</span><span> = 3+ √3</span>