Разность прогрессии:
d = a₂ - a₁ = -3,3 - (-3,6) = 0,3
По формуле n-го члена:
а₁ + d(n - 1) > 0
-3,6 + 0,3(n - 1) > 0
0,3(n - 1) > 3,6
n - 1 > 12
n > 13 ⇒ n = 14
Ответ: начиная с номера 14.
<span>x</span>²<span>+x+1=15/(x</span>²<span>+x+3)
x</span>²+x+1=t;
t=15/(t+2);
t(t+2)=15;
t²+2t-15=0;
D=4+60=64;
t1=(-2-8)/2=-5;
t2=(-2+8)/2=3;
x²+x+1=-5;
x²+x+6=0;
D=1-24=-23<0
или
x²+x+1=3;
x²+x-2=0;
D=1+8=9;
x1=(-1-3)/2=-2;
x2=(-1+3)/2=1.
ОДЗ:
x²+x+3≠0;
D=1-12=-11<0, x∈R.
Ответ: -2; 1.
M⁸ - 6m⁴ n⁵ + 9n¹⁰ = (m⁴)² - 6 m⁴n⁵ + (3n⁵)² = (m⁴ - 3n⁵)²
36x¹² + y⁶ + 12x⁶y³ = (6x⁶)² + 12x⁶y³ + (y³)² = (6x⁶ + y³)²
![\frac{1}{225} a^{6}-2 a^{3} b^{2}+225 b^{4} =( \frac{1}{15} a^{3}) ^{2}-2 a^{3} b^{2}+(15 b^{2}) ^{2}=( \frac{1}{15} a^{3} -15 b^{2}) ^{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B225%7D++a%5E%7B6%7D-2+a%5E%7B3%7D+b%5E%7B2%7D%2B225+b%5E%7B4%7D+%3D%28+%5Cfrac%7B1%7D%7B15%7D+a%5E%7B3%7D%29+%5E%7B2%7D-2+a%5E%7B3%7D+b%5E%7B2%7D%2B%2815+b%5E%7B2%7D%29+%5E%7B2%7D%3D%28+%5Cfrac%7B1%7D%7B15%7D++a%5E%7B3%7D+-15+b%5E%7B2%7D%29+%5E%7B2%7D++++++++++++)
1. (a^2+b)(a+b^2)= a^3+a^2b^2+ab+b^3
<span>2. (a^2+2b)(2a+b^2)= 2a^3+a^2b^2+4ab+2b^3</span>